Just because she's biting does not make her disposable. I assume your children probably do things you don't care for either, but you aren't going to give them up for adoption.. At the end of the day, rats are still animals, and some animals bite. You must be responsible to the pets you bring into the home.
First, take the rat to the vet. What if she's injured in some fashion and that's why she's showing aggressive behavior? It could be something you can't even see. I'd get her checked out just to be 100% sure.
Second, I'd move the rat cage away from the children, period. Put the cage somewhere where the children won't terrorize the rats.. not just by poking at them, but by screeching and running around and basically scaring them with their behavior. Let the rats have a peaceful place in your home that is insanity-free. You have a 2, 3, and 6 year old according to your posts.. that's a lot of craziness for small animals.
Don't ever letting your kids stick their fingers in the cage. They are too young anyway (your kids). If the rat was being nice and social then maybe I could see letting them interact with it, but a scared rat who is biting should NOT be handled by young children until an adult has worked with it long enough to curb at least some of the behavior.
That is strictly my opinion as a long-time animal-owner, so this isn't rat-specific. If I had a cat or a dog who was being aggressive toward a child, that animal would not be allowed to interact with the child until an adult got ahold of the situation. Then and only then should the animal be introduced to the children.
Only let the adults work with the rat until she comes around. That much is obvious, as you don't want the kids to be bit. You don't want ideally for the rats to bite adults either, but someone has to do it, and obviously it's the adults not the kids who have the responsibility.
Never let anyone stick fingers through the bars. Put a hand in the cage and leave it on the floor of the cage and let the rat check you out. Don't chase the rat around the cage with your hand. If you can avoid it, don't try to pick the rat up by coming up behind it, some of my girls are skiddish and they hate that and will freak out (no biting though) if approached from behind. I always try to scoop them up with two hands, one from either side, so they can see what's happening.
I had a biter years ago.. I'd lay my hand on the bottom of the cage with a treat in the palm. She'd come up to my hand.. and bite my finger. What I did was not flinch and not remove my hand. After that, she started to learn that the hand wasn't something to be afraid of. She started to see that there was a treat in my palm, and she could totally bypass biting my finger and head straight for the treat. By not retracting my hand in a jerky fashion, and by offering something pleasant, she didn't feel the hand was a threat. I can't say for sure if this is an acceptable tactic or not on the whole, but it did work for me.. and it quickly helped her behavior a lot because after that I don't recall being bit.
I think the most important thing here though is that this rat is doing something in his or her nature and should not be punished for being an animal at the end of the day. It hasn't even been a month yet, and it could take much longer to curb the behavior, so I suggest you work with her every day and just keep on going. I strongly believe the behavior WILL change as long as you keep at it.
