2 MAJOR problems
#1) I would not allow the male kits to breed with the mom ... generally that is not a good breeding practice. Regardless of which of the males you place with the mom ... the "law of survival" (the natural instinct to reproduce) will allow the male kit/kits to breed with the mom, given the chance to do so.
#2) Then there is that other "law of survival" ... "survival of the fittest" ... this one can easily cause two or more males to fight to the death for the chance to breed with a female in season, regardless of the relationship and regardless of the fact neither can actually get to her. Yes, I have seen a father chin almost kill a son chin, due to the fact that there was a female in season in the same room, but in a different cage. The father and son had lived together for 9 months without a problem ... until the female across the room went into season.
You can imagine what might happen with 1 female and 3 males in the same cage ... mom might accidentally get caught up in the brawl and be killed.
If you want the mother to have another litter, I would suggest trying to figure out which one is the father and put him with the mother ... as for the other two males (their kits) ... to be completely safe, I would put each of them in a separate cage. Brothers have also been known to fight to the death over a female that is in season, but, in a different cage. In most circumstances I would not house 2 or more males in the same cage IF there is a female chinchilla living in your home also ... even if she is in another cage. The males can and often will fight over her, even if they can't reach her ... they can smell her.
If you look closely into the faces of each chin, you may be able to see the signs of an older chin over two younger chins. If you have close up facial pictures of each and will post them, maybe we can help you figure it out ... no promise, but we can try to lend a helping hand.
How old is each chinchilla?
Jo Ann