I don't know that it would bother me. I find myself saying "mom" and "dad" about our future child's parents ... though I admit it may be different once we actually have a child and are taking on the everyday parenting. The only thing I wonder about is what your DD thinks of this (or will think of it when she's older). Will she be confused? Or will it be obvious from context which "mom" and "dad" people mean? You could think of it like the "birth" part of the word is silent when those people say that.
Still, no matter what, if it hurts you or makes you mad, you're entitled to those feelings. If it matters a lot to you, correct them every time!
