My daughter did this when she was just a little older than your daughter. I was pregnant with my son at the time. It was awful. The logical grown up part of me would say over and over "she's not doing it to hurt your feelings, she doesn't understand, etc" but at other times I would just cry. Even though she's little it does hurt.
It has gotten better, although it did take a while. What I found was that pushing me rather than dad really backfired. So when she'd say "no, I want daddy to read me stories" and he, being supportive, would say "you're hurting mommy's feelings, let her read you stories" she would just dig in her little heels and refuse. And that actually hurt my feelings more. So I got to the point where I would just try to let it go and de-escalate.
More recently (she's now 3.5) she would demand daddy when I picked her up at daycare (which I do every day). It was such a button pusher for me. We've come up with some ways to avoid this behavior, and that makes it much better. The more she can talk the better it will get, I bet.
Hopefully this is a phase that passes quickly. I'm sorry you're going through it. But it's absolutely no reflection whatsoever on you as a mother. I maybe should add that I think that my daughter and I have a great relationship, in spite of her daddy-centeredness. Also, I now have a 15 month old son, and he seems much more attached to me, so my husband does have a little taste of how terrible it feels to be on the other end of the "no, I want..." demand. Not that I wish it on him, but I think he didn't really understand how upsetting it is until it happened to him. Good luck.