Well, I’m not a divorcee, but I am single, and I live alone. I’m sure most people mean well when the invite me, but it always comes across as if they feel I am:
a) incapable of cooking,
b) too stupid to figure out how to say kiddush, or
c) all of the above.
I don’t like going out. People look at me as if I just came from another planet when I tell them I eat my meals at home. It’s especially difficult during Pesach.
On the other hand, one woman (I’m not sure if she’s a divorcee or a widow) found out I do my own seder. She said it never occurred to her to do her own. But she was so happy that I gave her the idea so that she could have HER seder in HER home.
Not everybody likes to be invited. If you want invitations, ask for them.