Culling biters is necessary at times. But a mother biting with young isn't a reason to cull. A mother eating young is. Myself an my kids handle the rats an ASF daily. Biters to me are ones that when I stick my hand in the cage/tub the little monsters runs from the other side an bites me (use a Mechanics glove). I've culled all of the biters.
New mothers will bite if stressed. I handle them an the pinks with a glove hand first. Let her calm down an you can move her while nursing an take pinks off the nipple if needed. Yes, it takes time. I like to put new moms in their own tub no more then 48 hours before birth.
I have more problems with rabbits scratching the heck out of the kids an mean pigs. Bad pigs = good bacon
If you ever get up to the Eastern Shore of Maryland I'll give you a few calm rats or some ASFs for free.