Once my DD was over day sleeps, I enforced quiet time in your room instead. So effectively she's still giving me some space (and herself time to wind down), but I stopped worrying about whether she was sleeping in there or not. I had to make sure she understood she didn't have to sleep, but she had to play quietly.
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This is what I did with DD1 when she did not want to have a day sleep. Most of the time she plays for a while and falls asleep anyway. I also found that I needed to change up her bed time routine a bit to suit her a bit more.