L.L.
Gee. A Grandma who sounds like she really wants to see her grandchild and comes over to see the child...makes a point to spend time with the child...and only gets "little" things on holidays.
I'm sorry, you sound SO selfish. I don't even want to say it, but you do. My parents live across the country from me and my in-laws work two jobs apiece and I would just DIE to have someone come over a few times a week and play with my children.
And seriously..."She doesn't take us out to dinner or buy us things!" YOU are an ADULT!!! You said yourself she doesn't make enough to support herself!
And she WANTS to spend time with you on Thanksgiving and you're trying to find a way to "politely" tell her she can't come...because why? Try, "Sorry, Mom, but you don't spend enough on gifts."