bluetooth mouse conflicts

I'm a recent Macolyte/convert, and decided to buy a wireless mouse for my desktop iMAC 20" 2.66GHz 4GB. It worked so well, I got one for my kids' mac mini. Within a day or two I noticed either/or both computer/s would lock up. Mine worked fine unless the kidz' puter was on; it took me a few seconds to figure this out. I couldn't get their mouse to work at all, I turned off the BT mouse, plugged in the corded mouse, but the mini didn't recognize the new mouse. I ran downstairs, turned off my desktop mouse, went back upstairs and revived the BT mouse there. Everything copacetic.

So now I can run one mouse at a time, theirs or mine.

I don't have this problem with a Logitech BT mouse running w/ my macbook at the same time.

Both the mini and the imac say the mice are paired.

Besided selling one of the mice, where do you suggest I start troubleshooting?

thanks.

Norm