The baby hamsters are now living in three separate cages. They're starting to fight so we'll need to find homes for at least half of them.
When I took them from their mother, she was no longer tolerating them. She climbed up into her loop tube (if you've ever seen the tubing for hamsters and gerbils, it's a circular tube leading from the top of the cage) to get away from them. The babies were too small to climb up so she would pack her cheeks with food and camp at the highest point, only coming down for provisions. She seems much happier to have the cage to herself.
Initially I put the babies in two different cages, putting the first four I could catch in a ten-gallon aquarium and the two quicker ones together in a smaller wire cage. Later when I bought a new cage, I split the group of four into two pairs.
By luck, it turned out the the two in the wire cage were both male and the rest female. I hope that I caught them in time so that we don't have to worry about a new generation.