1. That Pull-Up is a license to pee!!!! If naptime is the only time during the day that your child seems to need them, then the 'readiness' is probably there. You may be surprised at how quicky they will stay dry thru nap once you make it clear that they will no longer be needing baby pull-ups, make sure they go before nap, and are given a lot of positive encouragement. PS: I am speaking from personal experience here with my son, as well as tons of conventional wisdom that I have heard. I too also heard that they are 'ready when they wake up dry....' NOT TRUE!!!!! My son had only 1 or 2 little accidents once I wised up and took away the pull-up. These things are a license to pee!
2. My child would also wait for a pull-up or diaper to poop. He learned to old-it. This set up a very huge problem with incopresis. Once a child can stay dry thru the day, I would recommend that once a child has the peeing down pat, that potty training involves pooping as well.
The bottom line is that when the readiness is there, I think it is best to take the diapers and pull-up away completely!!!! It is not going to help to keep allowing them to use these, and by sending mixed messages.
And, as everyone else has said. If they are not ready, then they are NOT ready. No amount of pushing can change that.
I know that some daycares only take children who are at least three and who are potty trained. If this is the case, and this is made clear to all parents who inquire, and they do not also provide daycare to younger children. Then that is Okay. But, if they also accept younger children who would then be graduated to the 3 year old program, then that is compleltely unacceptable and I would find another option. If the daycare has a no-diapers policy, and a parent enrolls a child who is not ready for that, then it is the parents fault, not the daycares fault.