What time does she have to get up in the morning and is she getting enough sleep?
It sounds counter intuitive but if my kids became overtired it was horrible to try to get them to sleep. At that age my kids were in bed by 7:30 because they had to wake up by 7:00 for me to get to work on time.
Kind of a side bar, but around here we have an early K cutoff of September 1st. If people think their kids are K ready but they just miss the cutoff, they put them in private K and then transfer them to public school for 1st grade. I’d be tempted in your situation.
If you’ve got the resources and desire, there’s absolutely no shame in hiring a night nanny. My best friend did it and still says it’s some of the best money she has ever spent.
There are big developmental leaps happening right around this time, too. So it might actually not be the nap at school. They’re learning independence and control and their imaginations start to really go crazy…and that can all result in more difficulty falling asleep. I’d try just letting her nap at school and not wake her up and see what happens at home.
I’m also a huge fan of Insight Timer. It’s a free app with guided meditations and bedtime stories. It’s primarily an adult app, I think, but there are lots of children’s stories, too. My wild-brained boy can struggle to go to sleep for hours most nights…but when he agrees to listen to a story, he’s out in less than 20 minutes.
My DD missed the cutoff for public K by over 2 months. I put her in private K because of the mandatory nap for pre-K. It did help that her daycare offered K and their cutoff was later. There were some kids that did private K with DD and then repeated K at their public schools. Some moved on to first so you'd really have the choice.
I also birthed sleep haters. My DS sounds more like your DD. He doesn't like to go to bed. Once he's in the bed, he sometimes doesn't settle down for over half an hour. One of us has to stay in the bed with him otherwise he'd be pulling all the antics. It's not a great habit since he is now 5 and still won't relent on going to sleep alone. I tell myself the old "this too shall pass" cliche but it's hard to be wistful when you're in the thick of things. It doesn't help that my husband told him there are monster deer in the attic so now he really doesn't want to enter his room alone at night. While extremely annoying, I also sort of get the reasoning behind the monster deer because our children are also completely resistant to bribery and sticker charts at home (DS is all about the sticker chart in school, of course).