- All wealth is spread fairly evenly, no one is allowed to exceed others by any larger amounts.
- Excessive wealth in a family is confiscated.
- No loopholes are allowed.
- Your humans age and develop exactly as real humans (assumed).
- People become adults at the age of 18 (assumed).
- Resources are finite (granted, unless they live on an infinitely large planet).
So, what you say is that every day, week, month or year (or however often), each person get X amount of resources. Exactly how you divide the resources and which amounts are not given in your question, but detailed information is somewhat irrelevant; I guess your society will give a minimum amount to everyone regardless of what they do and those with a job will get slightly more.
You ask for the size limit of a nuclear family, something Wikipedia defines as a monogamous relationship between two adults and their children; while there are differences in the definition regarding the children (some only counts biological children while others counts all), I will count all of them.
As it is, a woman can be pregnant relatively early on after pregnancy depending on a combination on genetics and whether she breastfeed or not (the prolactin hormone, which is stimulated by breastfeeding, prevents ovulation), but I would say that a reasonable limit would be to say that a woman can only bear a child every 1.5 year (she will need some time to heal and be with the new born, it will take some time for the ovulation to start, not all attempts at becoming pregnant will succeed and constant fertilization treatment to increase chances will have a huge toll on the body). Once the children becomes adults, they would no longer be part of the nuclear family; instead they would try to start their own. This means that a family cannot really consist of more than 12 children unless they start getting twins or triplets. While twins are not too uncommon, triplets are relatively rare. Lets say that it will be hard to get more than 15 children in a family before the oldest one move out from the family. The woman will essentially never work, she will either be pregnant or on parental leave (yes, one can work while pregnant, but if she will be constantly knocked up, she will want to take it easy to spare her body).
So, will there be people who tries to be really super rich?
No, there won't.
Even if people were to try to make larger families than 2 adults and 15 kids, then they won't be super rich. Your own premise states that excess wealth in the family will be confiscated, so any resources larger than what the family needs to survive will be taken.
But if they buy kids from others or use surrogates or some other way? No, your premise stated "no loopholes", so however people tries, they will not end up with more resources than the family needs. One can also argue around whether those children will be really part of a nuclear family or not, so they might not even get any resources at all from them.
But, if they somehow manages to make more than the 15 children, then they should be super rich, right? Still no, once the children becomes adult, they are no longer part of the 2 parents X kids equation and their resources are their own and not their parents. Should the parents request that their adult kids give them money, then the first premise states that the surplus will be confiscated.
Also, you should consider that there is no reason to give X resources to each child. The children will not require a lot of resources for themselves, whatever they cost when it comes to food and clothes and such can be covered by a much smaller amount; the family will gain enough per child to cover the expenses but won't become rich by having a lot of them. As there are finite resources, this would be one place where they are saved. Once the kids are adults and move to their own place, they get the full amount of X resources.
Another thing to consider is that if the society managed to divide resources in a fair way so that everyone have roughly equally much, then eventually the mindset of the people will be so that no one strives for a lot of it. People will not desire more than they need.
Societal limits to size of nuclear family? I'd say "less than 20". I see no reason why any family would strive to be as large as possible. My guess is that parents will be satisfied with somewhere around 1-3 kids each, some might want more because they love kids and some will not have any at all, so the average would likely be 2 kids per family.
There will simply not be any super rich families that does whatever they can to increase their wealth, people would be happy to live in a family of a size that is manageable and not strive to increase their resources as much as possible. If you wish this to happen, then you need to change your premises (in a different question!) to allow someone to become super rich despite the system.
Edit (Since you added a case study of how one family got super rich):
In the case where one family (or a few families) manages somehow get super rich essentially over night, your proposed solution is a weak one. The way you make them super rich is based solely on that you want that to happen, but it doesn't make sense from the premises you give.
1) Why would the government allow people to have jobs where one can get super rich without already having a mechanism to confiscate excess? If they are allowed to have the ability to earn so much from ads or similar, then there would already be a strong progressive taxation on income. If they were to earn 10000X resources per adult and the state only tolerates someone to earn up to 10X resources, then they would have to pay 100% taxation on anything over 10X right away. There would be no such thing as "spend it however you want", they would simply say "hand it over, now".
2) If there, for whatever reason, is no taxation on excess income, then it's still a weird case. Why would the government allow them to spend it over a decade without any kind of limitations? That wouldn't work with such system as you desire, it's like the government is saying "only those super greedy can be rich, the rest of you cannot. If you are smart enough to shuffle your money around every 10 years, you can keep whatever you want". It's more likely that they would would give them three months or until the end of the year to spend it.
3) Why would the government allow them to get 100 kids?
It's biologically impossible for them to get that many kids and the government cannot be so ignorant that they will not understand that such excess of children is solely for the sake of keeping a lot of the money. The easiest way would be to state that bastard children will not count (while it is possible to harvest a lot of eggs from the original mother, harvesting over 100 would be too great stress on her body). Even if they were to count all those children as true family members, it's likely that they would intervene and say that it's not okay - not for the sake of the money but for the sake of the children (if the government is aiming to be even remotely humanitarian, if not then it's still not allowed as NO LOOPHOLES ALLOWED!). No parents would be able to take care of so many kids in a way that would be healthy for the children, most of them would be neglected. As such, you want them to form a "family business" where they hire full time care takers for their kids, but then again, why would the government allow all of them to be counted to the same family? If 90 of the 100 kids live their whole life with their nanny instead of their parents, then the nanny-kid constellation would be considered their own families. And it wouldn't be cheap, so they wouldn't earn as much as they want. Building a large enough house to fit everyone is going to be really costly. Hiring full time nannies will be really costly (you will need one per three children if you care about the children, plus extra to cover for vacation and sick days). Feeding and clothing them all is going to be less than the house costs, but still costly. Sure, the greedy father will likely want to do it as cheap as possible and have extremely shitty conditions, although if the government cares about it's people, this wouldn't be allowed. Also, why would the mother allow it? You stated that she was not the greedy type - she should outright refuse to build such large family for the sake of greed, especially if she has any motherly feelings for the kids.
It seems to me that you wish to have present Earth type of world in which you mix hardcore capitalism with extreme communism. It's not a compatible mixture. The way you have set up the question highly suggests that you want the system to be so flawed that this would work, but such flawed system would have a hard time to exist without collapsing. If you have a type totalitarian state similar to that in Nineteen Eighty-Four, then it could exist and be flawed as it wouldn't care about the well-being of it's inhabitants. But then they would be much more aggressive in fixing any problems that arise.
There might not be an outspoken limit to kids but that doesn't matter as there is a biological limit to how many kids a family can get. Getting massive excess of children would be noticed and deemed as not allowed as the premise states "no loopholes".
The state wouldn't allow your proposed situation to happen. If the state is truly there for the people, there would already be laws preventing your case from happening. They wouldn't have enough time to gather any larger amount of kids. If the state doesn't care at all about the people, then they might allow it for the heck of it; if it threatens the state, they would deal with it.
Your society cannot exist in the way you want it to exist. You are trying to mix incompatible ways of running a society and need to skip parts of it to make it work. If you go more towards capitalism, then who would care if there are excess wealth. If you go more towards socialism/communism, then the shenanigans you propose wouldn't be allowed as it would harm innocent children and it would destabilize the balance. If you go more towards totalitarianism, then who cares as long as they do not threaten the state; if they threaten the state, they would be executed since the NO LOOPHOLES rule would be more important than their lives.
In short There would be a limit of 20 children per family, more than that would make the system collapse. And still, extremely few families would aim to get that many.