Chibi_Star,

Mama cats, when they feel that their babies are threatened, will try to move them. The one thing you should do is get a deep cardboard box. Cut a "U" shaped opening so that the mama can get out and take a break from her babies, but leave enough of a "lip" on it so the babies can't crawl out. Or you can do what you've been doing, blocking it so Ozz can get out but the babies can't.

I have two questions. Does she try to put all her babies in the closet or just the one kitten? How old are the kittens?

To answer your questions:

1. No, she won't kill her babies.
2. She's probably moving them because she feels they'd be safer.
3. Yes it is normal for kittens to move around (depending upon their age).
4. Yes, it is normal for the mama.

Stay calm. Ozz will sense your stress. She might be trying to move them because you are handling them alot. If you need any more help, please let me know. And good luck!