I'm jumping in late, but here's my advice...
How big is the cage, is it a small sized petstore cage? Having a small cage can lead to aggression. I would suggest, if you have the space, to look into building a larger NIC cage:
http://rabbitsonline.net/view_topic.php?id=15348&forum_id=21
The holes are too big for babies, but I've used them before, you just need to make a baby bumper ( cardboard, or a smaller hardwire cloth). You could get a good decent size cage for under $100 easily.
The babies should also be in a nest box of some sort. If you don't have a wooden one made, a shoe box will work well. You can put a little bit of litter at the bottom to absorb their pee (although they won't make that much mess for the first few weeks), then take a bunch of hay/straw and fill the box. Compact the hay and make a fist sized hole in the middle. Transfer the babies and as much fur and hay from the orginal nest into the new box.
Don't use towells or any fabric that could produce threads. A baby could get themselves caught up in the thread and choke themselves or get it wrapped around an appendage and lose it.
I take babies out every day so they get regular handling and are friendly by the time you have to rehome them. When they are in a box, you just remove the box and you can handle the babies and put the box back in after. You should be checking them every day (multiple times a day) to make sure none have escaped the nest box or are injured/dirty.
Take a read of our Breeding and Care of Young section in the Rabbit 101:
http://rabbitsonline.net/view_topic.php?id=12047&forum_id=17
If you have any questions at all, please ask us!
--Dawn