I don't think this is something that can be medicated away. Having her personal physician do a mental status exam might be a good idea, so that it can be documented that there is reason for concern about her orientation to reality, which seems to be impaired. In her meeting with her doctor, she may or may not display the delusional thinking that you have described. It seems that she may not be totally deluded and actually fully convinced of the nutty things she has alleged. Some of this may simply be "trouble making."

Regardless of what formal diagnosis she might be given, she still would have a right to call cops and social workers. They still would have an obligation to investigate her allegations (though they have some discretion, if she calls them repeatedly with baseless allegations.)

Actually, the best thing that can happen to protect your reputatio s is for her to keep making lots of preposterous allegations. The cops and social workers are not going to keep chasing after crazy allegations forever. They will document that this lady is abusing the system making allegations that are without foundation.

I once new an elderly lady who couldn't stand for her daughter to go away on vacation. Whenever the daughter went away for a few days, the mother would call the police and report her daughter as a missing person. The cops did catch on.

Be careful how you describe your mother. You describe her as delusional, but you say she is lucid. Who manages her financial affairs? Is she in need of a guardian being appointed? If she's managing her home okay, then she's basically in tune with reality. Telling lies isn't the same as being psychotic. It can get murky.