I'm sure I'm not the only one, but it can get very confusing trying to figure out if Eunice is Lisa's or Oliver's mother. Especially if someone hasn't seen the episode where Oliver says "But you're my mother." Also Lisa calls her "mother" a lot.
She treats Oliver like Fred Flintstone's mother in law treats Fred. Eunice reminded me so much of her.
As I recall, the first time Oliver's mother was featured, we were supposed to not know that she was his mother, not Lisa's until he declared, as you stated, "But you're my mother." I believe that was supposed to be a big laugh line the first time through.
I think in the other episodes it was always clear that she was Oliver's mother. She just happened to love the city life and got along superbly with her daughter-in-law.
It was certainly not rare in those days, at least, for people to call their parents-in-law by the same names their spouses did, e.g. Mom, Dad, etc.