Bad breeder rat + fighting

I have two cages set up for my breeders which have pretty much become pets too. I've been letting them all exercise together since i want babies as feeders which has turned out terribly.
The females fight each other sometimes but the two males are constantly at odds.
Then, I've been taking the rat who has pups and giving her some out of cage time and she went up to her cage on thevoutside. A baby was on the inside with her nose up to the bars and she bit it on the nose! Obviously I'm just breeding for food and not disposition but what would the rats motivation be for biting her own baby?

She wanted to pull the baby out of the cage. I don't think these are bad breeder rats, I think you need to study up on rat behavior and breeding. I don't mean this in a rude way, just stating plain fact. Are you putting the 2 males together with the females? That is a no-no. You mention 2 cages.. which ones are in which cages? What do you mean when you say they 'exercise together'? When a mom has pups she probably does not want time away from the babies until they're 3+ weeks old. I would encourage you to do some more research on the rats and learn from the behaviors you observe and then learn how to correct them with your own behavior. Good luck!

Ok I thought maybe that's what she might be doing. The babies are about 2.5 weeks old. I just read an article stating that the mom may want time away from the babies and especially now since the babies are everywhere.
This is my first litter so I'm still learning...

She also still wants to be protective, so she may be trying to "save" them by attempting to carry her young off.

It tends to be rough reintroducing males or females for that matter multiple times too. Rats develop a "pecking order" of sorts and a single colony scent (they mark each other). When they are apart for long periods of time, the order changes and the rat that was away no longer smells like part of the pack. When you reintroduce them, they have to "sort out" who the boss is, etc. Being with females will also make them want to fight for rights to breed with them. Some males are more aggressive than others also, so if you have a more laid back male that is less aggressive, you might want to use him for breeding.

I think most people either house the males together, take one out to breed with the females, then put him back, or leave the male with the females and not house him with another male (or move him from female cage to female cage as they need to).

Good luck!