Admit it to yourself, OCDmom. You DON'T want to give up your nap during the day. You just have to figure out how to shorten it. Well, so far, setting an alarm hasn't worked.
How about keeping awake until your daughter naps ahead of you and you get up to do some more chores before you finally take a nap beside her? And then your nap will not be so long, because your daughter will wake you up not long after, because she's through with HER nap.