How old are the babies and what the cage like? Also what is your main cage like and how many rats do you have in it? What are they like and are they related to mum?
I would keep mum and young babies in a nursing / small cage until about 2.5-3 weeks old, by which time the babies are moving around a lot and benefit from a bigger cage. I wouldnt move mum in with her old cage mates at this age unless there was only one or maybe cage mate who was closley related and very calm/tolerant or it was with another nursing female who was again related. PLus at this age a really big cage may not be suitable as babies are not very agile.
At about 4-5 weeks you need to split the boys off from mum, depending on the group you are going to move into you could consider putting mum and the girls in with them, though personally i wouldnt as soom females can get very annoyed by babies pestering them (i tend to leave girl intros until the babies are around 8 weeks old for this reason). The boys will need another cage at this point
