How do I explain to my mother who has dementia that the Skilled Nursing Facilities is the best place for her to be?

My mother, Lois, is 83. She had a stroke in Aug. 10, 2010. She has aphasia & dysphasia. She was in the hospital for 3 days, then to a Rehab for a month,
then asked to go home. The doctor said she needed 24-hour care & could no longer drive. We tried home for a month until she said "okay, all of you need to leave. I can be alone now. I don't care what you or the doctors say, I say I'm fine now." So it was off to an AL. She seemed okay for a few months, then forgot to sign out, escaped twice, and begged strangers on the street to take her home. So, she was assigned more caregiving assistance, and her rent went up $500. I took her out 3x's a week, she wanted to go to her home to "get her things together" so we did that for a few hours every so often, out to beauty shop apointments once a week, and for pedicures every 6 weeks, shopping, etc. Then, one day when we were coming back from an outing she insisted on bending over and picking up a dime on the street and she fell in the parking lot. A few weeks later she fell in her room, then two days later fell again in her room and broke her back. I'm concerned about sending her to another AL facility for fear that the ratio with the staff and patients will not be as nice as this Conval./Rehab she is currently in. At this time, it is always reassuring that she is as safe as can be. But, the Conv./Rehab seems to have much older-looking, more needy patients. She doesn't want to live with us; not much seems to go on at Board & Care homes. The Conv./Rehab seems busy and my mother has a roommate which is nice. When my mother constantly asks when she will get out and if she can go home, I have a terrible time trying to answer. My visits with her are becoming frustrating and exhausting. Prayer, listening to our Christian radio station, and going over verses help during this time; however I start feeling confused myself and frustrated and second guessing myself--no matter what situation she is in. She really wasn't that happy at home--and was beginning to become seclusive--only wanting to see me (I'm an only child) and her grandchildren who are very busy living their lives.

My prayer is that my mom will be content at this Rehab/Skilled Care and happier with her new roommate Doris who she is going to try to stay with starting today. When we met Doris today, Doris made it clear to us that as long as my mother didn't watch alot of tv, didn't talk to much, and didn't snore, and didn't mind it if the door was closed at night, she was welcome as Doris' new roommate.

The verse "our hearts are restless until they find their rest in God" is having more and more significance as I see my mother and others try to find their happiness and rest in earthly things.

I also think I am beginning to understand why she insists on always eating her dessert first. As things are being taken from her--her health, her possessions at home, her continence, her ability to make rational decisions etc. it is really the only thing she probably feels she has control of. Thank you for this site and for allowing me to vent a little:)