To wake or not to wake?

[Purplehonesty]

My 2yo dd has a nap in the afternoon around 1/2pm.
The problem is she would sleep all afternoon if I let her and then doesn't want to go to bed until 9pm and still awake at 10.
If I wake her after an hour ish she will then be asleep by 7.30/8pm and has a good nights sleep and wakes up happy.
However when I wake her she is so upset; she cries and and screams and tries to go back to sleep on me and wants to be carried around until tea time. I'm trying to cook the dinner with her wailing up up up and crying on the floor if I don't hold her.
What's the solution? Leave her longer? Wake her earlier? Leave her be and let her wake up naturally and then face bedtime hell?!
If she doesn't get a nap she is awful to deal with, cries all afternoon with tiredness and after a few days she is thoroughly miserable so she clearly needs the nap.
I've tried cuddling her for a while (she goes back to sleep) a biscuit and drink, toys, games, going out into the garden but she is having none of it. Only up up up and crying.
What to do?

Can you do.something energetic in the morming (swimming, big playpark or similar), lunch at half eleven and down for a sleep at twelve. Still wake her for three, but its an extra chunk of sleep which may be what she needs.

My ds is almost 2 and he has lunch at about 11.30 and naps from 12-2. Bed at 7.
If I was you I would aim for an earlier nap and wake her after 2 hours.

Great advice both of you thank you. Will do that. After the summer holidays she starts Playgroup 9-11 so that should do the trick and tire her out.
Until then I will find something energetic to do as you suggest.
Thanks