Hi edwjr..

...and welcome...
What you are going through with your mom is soooo common..For so many different reasons a lot of parents do this to their children.
You did not mention what her health problems are..Perhaps some of it is fright, anger and frustration at herself for losing some of her independence, or it could even be compounded by some meds she is on?
If you are set in your decision to not move in with her then you must convey to her this, in a loving way, explaining why, and as hard as it is, not let the guilt get to you too much. My father is good for his guilt trips(I am an only child too), but I try to handle with with a sense of humor, and usually by doing that, I win out..lol.
It is hard to make someone feel guilty when they are putting you in such a good mood.
Some of this too comes from the generation they were brought up in, where parents ruled the family, no ifs, ands, or buts. When they became elderly some family member would take them in and that is where they would live out their years, way back there was no such thing as Home Care, etc.
It does take a bit of perserverence to overcome this guilt feeling, mine still creeps in there at times, but I know my dad knows I care, and most times he does it just out of frustration and boredom.
Our relationship seems a lot better now too, now that he can see I am going to stand my ground, he knows I would never let him down with anything important, but he has come to accept that I have my own life too, which does not mean entertaining him on a daily basis.
I think there are some caregiving articles on this site pertaining to guilt..they might help some too...But you must somehow work through your feelings or have them eat at you forever...
Let us know how you are doing...
Take care....
PrairieGal