lazy,
There is a special category for [something like] personal caregivers if one were interested in immigration. I know you took care of your mom, but this would be business. Not the same thing at all, but perhaps manageable. It
is a way in, often successfully used by desperate 3rd-world people. The point being that it is an accepted--and not very critically examined--mechanism for entry and Permanent Residency. There are other categories which would astound an American that will go unmentioned here.
Instead, consider summer in Canada and winter in Florida. (Wait--hasn't this been done before??)
I think you would get along fine in Canada, weather permitting.
If East Indians ("South Asians" is the new buzz-word) can do it, a Floridian can. Canada is also a fairly mellow place for unconventional folks. I am comfortable here, but I am crazy (just not violent).
Consider an extended visit. Vancouver, Toronto or Montreal to start with. Why not? But, be careful. Canada isn't Oz, regardless of the natives ability to ignore reality. (No offense. I manage to ignore a large part of reality myself. I do arrange it so that it is not fatal or damaging to my pocketbook, however. So far.)
Cheers,
Gypsy