it's nearly impossible to have traditional mammalian live births without pregnancy and childbirth being major issues. I don't think any small or even moderate level of change can fix that without going into the realm of impractical. I can think of a few far more extreme approaches which would work, most of which involve doing away with mammalian reproduction for some other alternative.
- The simplest and most in keeping with traditional sexes is to have a uterine replicator. Females were originally evolved to carry children, but now of days the embryo is removed and grows within a replicator that better protects it then the mother can. This frees the mother from all the hardship of childbearing and puts her on effectively equal footing with the male. Of course this only works in a scientifically advanced society
Biological uterine replicators. Perhaps the species has evolved to utilize another creature as their replicator. Think of how female kangaroo give 'birth' the the baby within weeks of fertilization, but what is born is not able to survive on it's own without living in the mother's pouch. Now imagine if instead of using the mother's pouch you used another species as the 'pouch mother'. This would do the same thing as uterine replicators, and be allowed in less advanced societies. Now how to justify this is still an issue. there are a few ways
- A) Domestication. Have a creator that evolved along a similar path to your protagonist species, but is not sapient itself. Think the difference between humans and monkeys. However, this species has evolved a pouch and a similar reproductive method. It could be domesticated and it's pouch used to raise the young 'joeys' of your species. If domesticated awhile ago it could be bred to be a better brood mare for your young. I actually really like this idea and think it would be pretty cool to see implemented now that I thought of it.
- B) Symbiosis. The two species evolved a symbiotic relationship long before sapience occurred. This is actually difficult to do in a believable manner, but I could think of a few ways to do it. If you really are interested in this post a follow up question and I could explain some believable ways to have such a symbiosis occur. The key point is that the species has to gain quite a bit from your protagonist species for it to benefit from such a specialized symbiosis. Personally I think the domestication option is far more viable, and offers an interesting bit of world building without require rethinking the evolutionary psychology of the species.
- C) Symbiosis again, but this time symbiosis with a plant that is not sapient. I think this sort of symbiosis is actually more believable, though still takes work to implement. The plant may very well depend on the protagonist species to care for and nurture it entirely. Strong symbiosis between plant and animal has existed, to the point that one can't exist without the other, before. Still, this idea works better if your protagonist species is smaller and tends towards having more than one at a time with a few of them dying. R-selective species are more likely to develop a system that is dependent on trusting an outside force then a K-selective species. It makes more sense if the species started out heavily R-selective and then adapted to more of a K-selective approach only after it started using plants for child-rearing. This implies many other species would also use plants for child-rearing. It also works better if the species still have some elements of R-selective species, such as having twins and triplets more often and possible being prone to one or two young dying at an early age.
- Have the species able to transfer the young between male and female, the way the seahorses do, and each trade off carrying the young. Maybe both male and female have pouches and regularly transfer the 'joey' between them. Perhaps it's difficult for one creature to carry the 'joey' to term, thus forcing a couple to have a child which could in turn have interesting effects on the concept of nuclear family and what a 'deadbeat dad' means.
- Have the species lay eggs, and take turns caring for the eggs.
- Have a species that employs a combination of R and K reproductive strategies, so they invest very little effort into rearing the child during the original vulnerable stage, and can provide equal effort into later rearing of the children that survive (see my edit below)
All of these are extreme changes from the norm, but these are the only ways I can see to keep pregnancy and birth from being a major difference between the sexes. Similar ideas can be come up with, but the key point is you have to move away from our sexual reproduction to a system where the female does not do all the carrying of the child as it develops.
Other approaches that are slightly different and lower, but not remove, the disparity of the mother are:
Have the children be born very undeveloped and tiny (but not nearly as bad as the kangaroo example where you still effectively need someone to carry the child in a pouch) so the mother doesn't carry the child as long or is as disabled by it, but the parents have to work together to care for such a week and underdeveloped infant. This is hard to justify except with species employing a hybrid R/K reproductive strategy (see below), but there is room to vary how much they lean towards R vs K.
Remove sexes and go with hermaphrodites that perform each role. This in turn allows the concept of mating leading to both carrying the child, to concious choice as to which will be the 'female', or to sexual conflict where both 'fight' to be the male when mating (look up penis fencing for an example). The latter would still have an interesting level of sexual conflict, the ones currently carrying children may even be seen as 'weaker' for loosing the sexual conflict.
Make it comparatively easy for one sex to change to the other sex, thus allowing them to pick their preferred sex. many fish and amphibians can do this so it's not impossible. Though again such an adaptation would require rethinking other aspects of culture and evolution that would occur due to it.
EDIT (indirectly inspired by falco comment):
I wanted to add an aside about R vs K reproduction. R reproduction implies having lots and lots of young, K involves having a few young that develop extensively. Generally sapience is something you would expect only from the K reproductive strategy. Our brains are a huge cost. They are what make childbirth harder, but more importantly they require a much higher energy cost, requiring us to consume far more nutrients, and take longer to develop. Instead of being born with instincts that let us survive on our own we need to learn everything. The smarter we will become the more helpless we have to start out as.
However, many of the reproductive strategies I listed are ones used by those that use the R strategy, having lots and lots of young that they leave to fend for themselves and expect to die out. The reason mammals carry their young for so long is because they have so few and are investing so much that they want to be able to help the young develop. Things such as relying on symbiosis with trees or other creatures as brood mares are very much R strategies, and even eggs tend a little more toward the R strategy, though plenty of species like penguins still lay eggs despite being a K species.
Simply put if you want a sapient species they almost have to rare a very small number of young with a high childcare cost, R strategies are not viable scientifically.
The easiest way to address this is to imply that the species started out as an R strategy and later evolved into more of a K strategies as sapience developed. However, this should still be evident. If the species uses R strategies they will likely tend to have twins and triplets, perhaps with a larger time span between litters, rather than one child at a time.
Another option is to say the species has a combination of R and K strategies. Maybe the species produces a massive number of young and force them to survive on their own originally, and only later does higher parental involvement occur with the remaining young that survive. Imagine a frog-like species with an intermediate tadpole phase. The mother births a massive number of young the same way frogs do, and they are left to develop as 'tadpole' like creatures on their own, with many dying to predation or even competition with their siblings. The parents then take a small number (no more then 5, more likely 2-3) that survive this phase and begin to invest effort into raising them. Thus there is little effort from either species in original childbirth, and equal rearing expense after they adopt the surviving 'tadpoles'.
I suggest a separate tadpole phase because brains are expensive, and R strategies don't work with highly intelligent sapient species. Thus they would have to have one phase where they are not sapient, animals like tadpoles, where they are simply trying to survive physically, followed by a metamorphosis into a creature the emphasizes intellect and brain power that still requires a high parental commitment to develop that brain power before it's self sufficient.
Many animals in nature employ strategies that have siblings compete against themselves to select the strongest to survive. birds will sacrifice their weakest, the weak pups often die in litters, hyena young will try to kill each other when their mother isn't looking, and there are species of sharks that actually fight and kill each other while still in the womb so that only one is born. It's plausible that this could evolve, less likely than traditional mammals, but could be done. It works best if you can explain why the survival as tadpole helps to select creatures that are more likely to have reproductive success as adults. The simplest strategy that comes to mind is imply a world with high mutagens, like radiation, so that the 'tadpole' phase is to filter out all the young that are born with birth defects or mutated to find the few that managed to be born 'normal' and healthy.
An even more interesting concept would be to have a species that doesn't always metamorph. Perhaps sapient adults birth hundreds of young which grow as smaller 'tadpole' like creatures. They pick a few of the strongest and somehow trigger the metamorphosis of those young into their sapient phase, these young will get high parental involvement and rearing into sapient adults. The remaining young are allowed to continue to grow and develop, and are even capable of eventually reproducing; but won't reach sapient. They are left to live in the wild and survive on their own, with little or any parental involvement, but can still become part of the non-sapient species breeding pool. This strategy combines both R and K strategies and offers some extremely interesting world building options. However, creating a world where this would evolve is difficult, and the implications for their psychology must be considered. I may post a world building question about this since I think it could be very interesting if done right. :)