Do you have a daily regular routine about "naps"? It being the SAME routine everyday... pre-nap and for naps.
By pre-nap I mean... leading up to nap time.
For me, I wind-down my kid(s) first. I warn them verbally giving them a head's up about it all, so its not "rushed" and not an "abrupt" change of pacing or forced. It takes me about 1/2 hour to wind-them down... then it is nap time, actually in the room and in their bed. That is the transitioning time... winding-down. Kids need that.
Nap for my kids, is at the same time everyday, pretty much. And they know the routine like auto-pilot. They will nap about 98% of the time. My son is now 3.5, and my daughter is 7. My daughter, for her being her age, will still nap on occasion. My son everyday. He needs it and I don't "force" him. He will not last the whole day without a nap. He naps 2 hours, and still sleeps fine at night at about 8:30. Both my kids.
And no, you are not selfish... but naps are important for a child. Even in Kindergarten they nap, and in preschool. A child needs it. Although I know some kids seemingly "give up" napping. Not that they don't need it, but that it is just too hard to put them down to a nap, or the child will make it without one. Not that they are not tired.
If your daughter has quiet time, that is fine. My son will sometimes amuse himself before actually falling asleep too. That's good. But, I always then tell him, "5 minutes, then nap..." and then he knows, then he will stop "playing" and then settle down and fall asleep.
Or, I will also be in the same room while it is his nap... and I "read"... but he KNOWS this is not time to play with Mommy. I don't engage or talk. I "read" and even close my eyes. And sometimes I actually fall asleep too. My son, knows, that it is sleep time. He has a routine and then will fall asleep. If on the rare occasion he does not fall asleep... he will tell me he can't. And he honestly can't. I know him. So I let him get up. But I tell him that if he gets tired later, he can nap. He says okay. And later when/if he IS tired... he will tell me... and then go into his nap routine.
Its just the routine of it all... I've done the same routine with him since he was a baby. So by now, well its just a "normal" everyday thing. Not forced... but I do go by his cues too. I know when he is tired. He knows it too. I don't treat "naps" as something bad or junk. It is just a routine.
My kids know that. I have not had a real "battle" about it nor when it is nap time or bedtime. It just is.
Again, it has always just been a daily routine, like brushing teeth or eating dinner or taking a bath.
Often, both my kids will nap at the same time too.
I have also, taught my kids that it is OKAY to "admit" that they are tired or need a nap. So they don't think of it as some kind of banishment or "punishment." So, now if my kids are tired, they will tell me/hubby... and we tell them its good to know themselves... and its not something "bad" to admit... naps are nice. So they don't fight it, if they are tired.
But all kids are different.
All the best,
Susan