DM used to say 'don't meet trouble halfway' and 'don't cross your bridges until you get to them'
I also just saw this one: Worry never robs tomorrow of its sorrow, it only saps today of its joy. ~Leo Buscaglia
all of which, of course, is easier said than done.
I think we do reach a point where we start to worry about our parents but we sometimes forget that they are people who have lived long, experienced a lot (probably more than us as DH's and mine lived through the war years) and are stronger than we think mentally, if not physically.
We tried to persuade MIL to change certain ways of living but she insisted she would carry on as she always had, so we carried on worrying about her falling down the stairs which, in fact, she never did.
If your mother was left on her own would she come to live with you or would she be happier staying where she knows best and where she knows people and has other family?
I can't advise you on how to stop worrying, sorry, as I am a worrier too.
However - I do not want my children to worry about us and I know that they have started to do that. Should we tell them about every appointment, every ailment, or not tell them and find that they get rather cross if/when they find out?
Perhaps discussing it with your mother would help? What she thinks, what her plans would be if she was left on her own? They may have discussed all this between themselves (but don't want to worry you in fact).
www.quotegarden.com/worry.html