Hi M.,
My daughter went through this at about the same age- and again about 6 months later. I tried everything to get her to sleep, and I realized you can put a kid in bed, but there is no way to make them sleep.
I decided that the rule in my house is we all have "feet off the floor time" each afternoon. We try to go potty, then do our nap time routine, and then I tuck her in- I tell her she does not have to sleep, she can look at books, but she has to stay in bed and keep her feet off the floor until I come and get her. If she can do it there is a little reward- maybe a sticker, or a walk to the park, whatever. The only reason to put your feet on the floor is if you have to go potty, then you go to the bathroom, but when you are done, we go right back to bed.
So I explained all of this to her, and she was excited (make it sound like a game)- when she was younger she would stay in bed and look at books or just lay and play with her doll and teddy- If there was no poo interuption, she would often end up fallilng asleep- with the interuption, she would get back in bed, and it was usually no sleep, but at least some down time. If she did npt fall alseep, I would go get her after an hour- make a big deal out of how proud I was that she kept her feet off the floor the whole time- or that she went back to bed after going potty, and then we would go do her reward.
So this started last January- She was 2.5. She had 3 weeks where she napped 1x a week and was cranky the rest of the week. This was when i was playing with how to handle it. She started napping again after 3 weeks, and did great until June when she had another 2 -3 week nap strike. I thought she was going to give it up, but I kept the routine in place, and insisted on feet off the floor time. She went back to napping again. This past month she has started napping 3-4 times a week, and reading books the other days. I think she may be starting to give up a nap (she is 3 and 5 months)but the way I see it, if I don't give her the opportunity, she won't nap, but if I do, she might. I think the down time even when she does not sleep helps (I know it helps me) and this way she feels in charge of herself- I give her the tools and place to nap, but she can choose to do it or not so there is no power struggle.
I hope this helps-
S.