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1. Your 31-month old has only known one place to nap for 5 days(?) per week - daycare. She's only seen the morning and possibly afternoon naps as something that is initiated by other kids going to sleep as well as the daycare caregiver putting her down to sleep. In other words, this is new to her. Maybe she sees time at home as "awake time!" I'm not surprised at all that she is aware that it isn't dark out and that's why she won't nap.
2. She's 31 months old. Many kids stop napping before that. I'm a father of three. Naps were no longer a "given" at that point. It was spotty at best. Like some others said, we'd do "quiet time" and that worked for a while.
Thinking back on it, my oldest stopped napping at 3 with any sort of regularity. My middle child stopped at 2.5 and my youngest stopped napping at 2.25. However, my youngest does still fall asleep in the car (he's almost 5). It's been over a year though since he'd fall asleep in the car AND then could be carried to his room to nap.
Point is, get ready for your little one to be part of your entire day. It happens. Your 2-3 hour kid-free time in the middle of the is coming to an end. Sorry to give you bad news.