Removing Cactus Babies?

The mother plant should be ok if each wound where the baby was detached is able to heal without getting problems such as fungal infection that would cause it to rot. A recommended way to help here is to lightly dust the wound(s) with horticultural sulphur powder. Also you can pot the babies: use a mixture of soil & sand. As an extra tip, charcoal is an excellent absorber of soil-based impurities, so you can take a small quantity (ordinary bbq natural wood charcoal is fine for this), grind it into sand-grain size bits & stir it into the babies' pot soil.