if I'm not mistaken aloe vera likes to be root bound. so If you're moving it to another pot you should probably put it in a slightly bigger pot but not anything much bigger though. to remove the babies I think maybe you should maybe lightly pull the baby away from the mother plant and repot it into a pot that's not HUGE or anything. ok I just did a little searching and this is what I found...I hope it helps some!
aloe vera care Repotting--Aloe Vera can stand being root-bound, so repotting is not
necessary until the upper plant gets top-heavy. When a plant gets
root-bound, it will send out more new shoots or pups. If these are not
taken out for replanting when they are 3 to 4 inches high, they will suck
the life from the mother plarlt, which will get bright green and spread
its leaves horizontally rather than vertically. The plants will grow in
any kind of soil but good drainage is essential. The pups should be
repotted when large enough, watered well and not watered again for about
3 weeks, forcing new roots to seek water. The transplanted pup may turn
grey or brown for a while, which is normal. New pups make wonderful
presents.
p.s.-you have to scroll down a bit on the site above before you get to the info on caring for aloe vera....and I almost forgot....WELCOME TO THE GARDEN HELPER!