Is there a device that is available to notify staff when an unwanted resident comes in?

She has a big imagination? Is any of this actually happening? If it is, I'd move her.

Sadly this is common in dementia facilities. The staff get to know who the wanderers are and who has sticky fingers, so it pays to have a good relationship with them. Realistically, even if an alarm sounded when someone came into your mother's room staff would not be able to respond immediately. Your best defence is to make sure your mother's things are labelled and don't keep anything valuable in her room. Take pictures of irreplaceable sentimental items to leave with her and bring them home... tell her they are being cleaned or appraised or whatever if she makes a fuss. As for the pushing, that should not be tolerated, aggressive residents need to be monitored as assault is not unheard of when reason and restraint are lost.

All she has to do is push the button on her pendant. Bear in mind these attacks may not be real, she may be delusional.