Her mother did not mention dinner? She did not invite you? Your W waited until her mother left and then told you she was going to her mom's? This was after them spending the day shopping?
Correct. See my additional post about why I though that dinner was coming at our house.
Her mom said "So I'll see you at my house." before she walked out. At that point I thought "you" was both of us.
I asked W if she is going there and she said yes. I asked if she would stay there for dinner, she said yes. I never asked if I was invited because I was not expecting that.
Her mother stopped coming over after the bomb was dropped and W started seeing her mom without inviting me.
I can see how that can be awkward under the circumstances. Her mom and I have been the best of friends.
