At around that age my ds had a sudden jump in how long he could stay awake before his nap. Her messing around & not sleeping is her way of telling you she's not tired enough when you try & put her down. Although there are some LO's who drop naps around age 2, many will carry on until age 3, & given she is still napping at nursery its unlikely she is ready to drop it. I'd just try a later naptime. 1pm is about average at this age. If usual bedtime is 7pm, yes you may find that with a 1pm nap she's not quite ready for bed. However I learned through bitter experience that it was better to accept a slightly later bedtime (7.30-8pm) until ds dropped his nap. Early naps meant refusal or early waking & capped naps meant very grumpy for rest of the day! Later bedtime is the lesser evil!
Why not pat or rub her? Better that than she's exhausted. She won't be napping forever and once she's over the sleep resistance you can cut it back.
I know people who end up with 2 year olds who only sleep in the car as they stopped self settling in a cot. I sat with ds at this age and he fell asleep just fine that way - better that than have to drive everywhere. They don't nap forever...
My two oldest dds dropped their naps bang on two years old. My third dropped about 50% of her daily naps when she turned two. On the days that she did nap, getting her to sleep at night was hell because she was not tired enough. Dd4 is 18 months old and still needs her daytime sleep.
It sounds like your daughter goes to sleep brilliantly at night. I would be tempted to drop her nap, or at least try for 10/15 mins then give up. My fear would be that insisting she has a day time nap may mean that you lose that lovely night time routine that you see to have.
I am very envious. My girls are terrible with sleep. Dd1 6 and dd2 5 are now good. Dd3 3.5 usually needs us to lie with her til she goes to sleep (though increasingly so knackered at nighttime that she will fall asleep quickly) and dd4 needs me to lie with her and hold her hand. It usually involves tears. On both our parts!
I am kind of looking forward to dd4 dropping her nap so that she is so tired at nighttime that she falls straight asleep! Good luck. I am sure others will come along with much better advice!
The past two weekend my OH and I have been fighting a loosing battle with our 22 month old fighting her normal afternoon nap and getting - at best - 20 to 30 mins of rest.
She still sleeps for and hour or more at nursery, where she is 4 days a week, and I know she is tired with us at the weekend but when we put her in her cot (as we have done for her whole life pretty much) she will sit and play and sing and chat rather than settle to sleep.
I fairly certain she couldn't cope with dropping her nap as she is always shattered by about 6pm, rubbing her eyes and unsteady on her feet and she asks for milk and stories!
Yesterday I could tell she was tired at about 11.45am while we were playing, so I asked her if she would like her lunch and to go to bed and she said yes! We did quick lunch and put her down to sleep before 12.30 and had chatting and mucking about for nearly an hour, then a tiny nap, then awake having done a poo!
I've tried putting her down later - closer to 1/1.30pm, which is the time she sleeps at nursery but if you factor in the faffing about then she doesn't end up going to sleep until after 2 which seem to late to be napping at her age.
She has been SUCH a good sleeper all her life and is still settling fine at night, we read a couple of stories, I tuck her up and she says 'bye bye mummy' and rolls onto her tummy (I do not expect this to last though!) I don't know how to help her settle during the day in the ways she always sued too. I tire her out, remove toys from the cot, her room is the right temperature and dark.
At nursery they pat/rub her but she's never needed that at home before and I'm reluctant to start.