In a situation like yours, the best you can do is to have your mother evaluated by a psychiatrist. If she does have dementia, it must be diagnosed. Then guardianship
should be sought for control of her assets. Of course she may not agree to the evaluation, so if not, I would urge you to contact Adult Protective Services in your county. This organization should be able to send a psychiatrist to the home to do the evaluation there. You could also call the Alzheimer's Association for other resources in your local community.
The early stages of dementia can be very challenging for the family and can cause tremendous stress. The disease has taken your mother's ability to make good decisions and to recognize her limitations. Set the wheels in motion as I described above and then reach out for some emotional support from a group or individual therapist. You and your sisters will need to find ways to recharge so you can deal with what's up ahead -- placement.