I agree, I think this parent is asking too much of their provider. I have also never heard of a nap at 2pm, it is so late.
I had a parent recently who wanted my daycare to accommodate her child's nap schedule- one at 11am and one 3pm, which basically means her child would be napping AROUND daycare naptime of 12:00-2:30pm. I will allow a transition weeks if it is ABSOLUTELY necessary and if the child will still have their afternoon nap, but after that I believe that the children should all be on relatively the same schedule, so that we can make the most of our day!