Whyyyy won't my toddler nap?

[Rockettrain]

DD is just turned 2, although in some areas she is a little behind developmentally and has only just started walking and can only say a few words.
She still very much needs a lunchtime nap. At the childminders, they have snack at 9.30, lunch at 11.30 and then she puts her down in her cot just before 12pm and she sleeps until 1.30pm at least, sometimes 2pm. Always has between 1.5-2 hours. She goes 4 days a week.

At home we try to follow the same timings in the mornings to keep her in the same routine. She goes off to sleep no problem but we are lucky if she will sleep 45 mins. Today she has done 30 mins! As soon as she wakes up she is standing up and dicking about in her cot, no chance of her going back to sleep, we try leaving her and she just messes around and starts shouting etc. We have also tried going in and shushing and telling her it's nap time still and she starts asking for books and trying to get out etc.
Help please!

Also the irony is not lost on me that at the childminders that nap effectively costs me ten quid (lighthearted, I know I am paying for the childminder to still look after her, etc etc)

Could she be more tired at nursery due to a busier morning? My LO does a better nap at lunch time if we have tired her out in the morning!

Dd is simillar although younger. Personally I think that she gets much more stimulation at nursery so her brain isn't as tired at home - trying to home school an older sister so it's hard to give her lots of extended play opportunities

I'd try and tire her out a bit more with a walk or ride/scoot somewhere in the morning to see if that helps.

Sorry should have said, she does the same even when we have spent the whole morning out at the park etc. It doesn't seem to be related to what activities we do or how much stimulation we give her (which was my first thought). I think the childminders may be more stimulating generally but even when we make a conscious effort to tire her out it still doesn't seem to work!

My DD only napped (for 30/40 mins) in the afternoon until they were 18 months.

At that point they outright refused, if we tried to get her to nap, she would in turn take about an extra hour in the evening to go to sleep. Resistance was futile, so we went with what she wanted. At nursery she would 'help' the staff tidy round while the other kids napped.

Can you introduce “quiet time”? I.e. this is quiet time, you’re either asleep or playing quietly in your cot with some books or toys you chose earlier. You can’t make her sleep but hopefully that will keep her recharged and still give you a break!

It's just nursery magic. All nuseries and childminders have it!

@catmandont I would understand a bit more if she was just refusing her nap generally, and then maybe think she doesn't need it anymore and is just dropping it. But she a) obviously still really needs it, and spends the afternoon yawning etc when she only has a short nap and b) will happily and easily do 1.5-2 hours with the childminder. So it's not like she's refusing generally! And she even asks to go for her nap just before 12. She likes her little routine. But at home she just wakes up again after 30-45 mins! Argh