Should I forget my daughter's father's birthday on purpose?

[Popsfav]

Yes, it will show him you are very immature.
Quit worrying about silly little things and focus on your child.
He is an ex, he isn't supposed to do the things he did when you were together.
Mother's Day is for children to honor their mothers. As I said in my previous answer, if it were a Mother's Day card, since the child is less than 3, it would have been a nice gesture for him to have helped the child pick out one, strictly from the child, but not from him. But, being as it was on line and FB, he couldn't exactly do that.
Get over him as he is showing you he is over you. You are simply the mother of his child. This does not affect the child in any way and that is all it is about now- the child!