You said in your first post that when she does nap in the car then the night is fine, right? It sounds like she does still needs a bit of day sleep. Is there a chance she will nap in daycare?
When my DS started daycare he was as well 2yo and he often refused napping there, but just the fact that he was lying down in a pretty dark room, chilling out, helped him with the evening.
If there is no way she will nap in daycare then I would try for a nap in the car or once you are back home. I would even AP it if needed.
Do you use AP at all? Sure it's not great, but often at the 2-1 transition which she obviously still going through there is no other solution.
If you know of an AP that will work for her could you try it for BT when she fights sleep (and is probably OT)?