J.J.
hi D.;; i'm just writing to give some moral support and to LOL w you; my 2.5 yr old son is still in a crib and gets up at about 5 almost every day and always has; he has always been excellent about going to bed whenever we start his night time process, be it 7 pm or 9 pm or anything in between; so i didn't feel i could really fight him on staying asleep. also he wakes up very awake like your daughter and i don't see how he can be coerced into going back to sleep if he's not tired. once in a while he will do us a great favor and sleep till 6 or 630, maybe once a month he sleeps till 7; he likes to cuddle in bed in the morning but never for long. ONE TIME he fell back to sleep in bed with me.
my 11 mo old daughter will usually stay asleep till 6-630 but she too, once sh'es up, that's it, her day had started.
i have NO advice for you, only compassion! but i would say that it's way too early to try the tape over the numbers thing; my friend w 3 kids does this but the alternative for her kids is that they are allowed out of bed, just not to come into mommy and daddy's room till the clock number is 7; however her kids are 6 and 4 and know all thier numbers, obviously. 2 is too young for that.
good luck to you!