Does sound like interference was the problem and exactly what happened
here when two wireless mice were operated relatively close. Some mice
have switches to alter the frequency band or sometimes it's a special
combination of button clicks to do it ( check the manual ! )so worth
looking into. We tried all sorts of things to eliminate the problem,
including the different frequency switch on mine and placing a metal
barrier in line-of-sight between receivers, but nothing worked 100%.
Symptom we had was moving mouse A prevented clicks on mouse B, though
the pointer could still be moved - and vice-versa !! I now use a wired
track ball and prefer it so my partner can use her wireless mouse now
without it suddenly being unable to click on anything.