I know exactly how you feel. My son is now 3 and has had this issue as well. Since I work at home his afternoon nap is essential. There are several things to consider:
- how much sleep is she getting at night? She might be meeting more of her sleep needs then. Because I need him to take a nap during the day, my son goes to bed at nine and I let him get up whenever he is done sleeping (for him that's anywhere between 6 and 7 am). So it's a trade off -- daytime sleep instead of one long nighttime sleep.
- how active is she in the morning? If I let my son watch too much TV (more than 45 minutes or so) then he doesn't take a very long nap. He takes his longest naps when we are up and active, especially if we go outside and play.
Because she is still taking a nap (you didn't mention if she is hard to get down for a nap) I assume she is ok with naps. If she won't sleep longer, just let her know that you both need quiet time until 3 pm and get her a clock that she can read. If she wakes up before then have her play quietly in her room.
Good luck to you!