Not sure what stage my Mother is at...is it time for Hospice?

My mother is 98, has no major medical issues with the exception of a heart murmur (Doctors and family have decided to do nothing about). She has undiagnosed Dementia. She was living in assisted living (RCAC) but recently had 4 falls within 3 weeks. She was admitted to hospital on Saturday and released the following Friday. It was pure peace of mind having her in the hospital knowing she was safe. The ER doctor's recommendation was SNF and the Social Worker's recommendation was Memory Care. My sister and I received a list of facilities from her Social Worker from Family Care (she is on Medicaid) on Wednesday and started looking at places, on Thursday the Social Worker (not same SW we met with as I think this one was on vacation and then came back) from hospital told us since a particular facility had an opening that they were going to release her from the hospital. We said NO, we were still looking and weren't comfortable with said facility. On Friday, they called (while we were driving around looking at places) and said they were transporting her at 1:00 to the place they picked. We called them back and said give us until 3:00 and take her to my house. She is at my house and basically has been sleeping since she arrived or on the toilet having to urinate. She can barely walk, is all banged up (knee) from her last fall, is very weak. She ate dinner yesterday (small amount) but hasn't eaten anything today since she has been sleeping for about 4 hours now. She said she is dizzy, feels like she is going to throw up. She did have a geriatric doctor but long left, now sees a doctor that comes to the assisted living home, he is useless. That is the background, my questions are how do I get a dementia diagnosis and does anyone in the State of Wisconsin have any experience with hospice for frail/elderly? -