So I'm not really sure whether I get it right or not, but apparently most mammals are dichromatic. Humans have three cones that detect light wavelengths, small for blue, medium for green, and large for red. Meanwhile, many other mammals have rods and tapetum lucidum, so they see better in the dark. From what I could find, mainly research based on dogs and cats, they both can't detect red. I'm not sure, but I'm somewhat assuming that since large wavelengths correspond to red, does that mean that most if not all dichromatic animals can't see them? So, if an animal were to have a better night vision (tapetum lucidum included), as well as a dichromatic vision, would they necessarily not be able to detect large light wavelengths (red)? I would much rather them not being able to detect small (blue) instead, and have a similar vision to tritanopia. Is that possible? If so how unlikely would it be?
Yes, it is perfectly possible for dichromats to see red wavelengths. The number of distinct receptor types has essentially nothing to do with the range covered by those receptors.
Even in the specific case of dogs and cats, I'm reasonably certain they are still sensitive to red wavelengths--they merely lack the ability to distinguish them from green.
Cats and dogs can see red light just fine. What they cannot do is distinguish it from green light. At the red end of the visual spectrum their limit is very similar to the humans, extending to about 750 nm. But at the blue end of the spectrum they may see quite a bit into what for us is invisible near ultraviolet, because their lenses absorb ultraviolet light much less than ours; their visual spectrum may extend to about 350 nm, whereas ours ends at about 400 nm.
See the discussion on the visual spectrum of cats on Biology StackExchange.
[Would a dichromat] necessarily not be able to detect large light wavelengths (red)? I would much rather them not being able to detect small (blue) instead, and have a similar vision to tritanopia. Is that possible?
Possible? I don't see why not.
AFAIU, the three flavors of human color blindness are caused by a lack of one of the three usual types of cones. Thus, an animal with two types of cones responding to similar frequencies as two of the three types of human cones would have vision similar to a person with color blindness. For the right set of cones, that would include tritanopia.
As far as possibility, this seems like a slam-dunk.
If so how unlikely would it be?
Well, here is where you have problems. At least in humans, the peak response frequencies of "red" and "green" cones are fairly close together. (I don't know offhand, but would suspect there is a biological reason for this.) One would expect that if an animal only has two types of cones, it would be advantageous for the frequency response of those types to vary as much as possible, i.e. we would expect blue and red cones, not blue and green.
However... it's also well known that rods are less sensitive to red light. This makes me wonder if there is a reason why animals with tapetum lucidum don't have red cones.
Anyway, the point is that you have an interesting question why your critter would have cones with similar frequency responses. Given that you are asking this question, you may already have an answer, but I would think you would want some reason why it is important that they can distinguish the colors they can.
BTW, while not directly related to your question, I should note that there are various software programs that claim to "simulate" color blindness, which may be of use to you. One (free in both senses) is KMag, although getting that to run on not-Linux might be a bit of a pain. I believe there are also online tools, though uploading pictures is a bit less convenient.