you could usefully take your mother to see a psychiatrist. neurologists don't deal with the thoughts people have, they deal with the physical brain. i'm sure that a good psychiatrist would indeed be able to figure your Mom out if, as you think, her mental health is an issue. it's not clear to me from what you say that she had an actual physical check-up with brain scan, mri and so on, to ascertain she has no brain tumor or other discernible factor. so i'd suggest all the following:
-- physical check-up with mri, brain scan and so on, to eliminate physical cause for her issues;
-- psychiatrist's visit to ascertain whether she actually has a mental illness (and you might give this some thought also, since most elders who present serious mental health issues have actually had them lifelong and usually family members have had some suspicions about this e.g. ask yourself if your mom has always been a bit paranoid, whihc could indicate lifelong schizophrenia;
-- seeing dead people is normal for elders moving towards death and it's not psychiatric;
-- breaking up the room is not normal, not even for dementia, so something really is going on with your Mom and you do need to get her help;
-- consider medications -- did she have a change of medication before all this started up -- some meds are very destructive to the normal mental well-being of some elders and she could be having an extended allergic reaction which affects her mental health -- not so unusual in elders, alas;
-- overall health checkup for her -- including liver tox test, oxygen test and so on, because these things out of whack make people look crazy;
-- i suggest you get a medical power of attorney form ready for when your Mom is feeling agreeable and see if you can get her to sign it, which would allow you to be present and to talk with the doctor.
-- as hard as it is, be very calm and not confrontational with your Mom right now, because that will give her confidence in you and get her to agree you should be in the doctor's office with her -- which is pretty normal for family and elders;
-- otherwise. you could go to court for a competency hearing, which no-one really likes to do, but sometimes it's unavoidable.
-- next time a doctor offers you to have your Mom admitted for a psych evaluation, grab the opportunity. it's not a threat or a punishment, it's a gateway to real help for all of you. don't back down because Mom "promises" to behave. You're right, your Mom has serious problems right now and she really does need your help, but you really need to know what the cause of all this is.
-- and maybe consider having your Mom move into care somewhere, perhaps a mental health care home, because you can't all go on this way. you need a sane life, she needs help. the degree of violence in her behaviors signals that she is in a serious health crisis. get a small camcorder and record some of this, then you have your evidence. or call 911 when she's acting out violently and then too, you'll have your evidence and she'll have her psych eval.
dont keep backing down. you need the help, and she needs the help too. it's not her fault, i'm sure, but you all need expert intervention here. please do it for all your sakes. blessings on you all.