Remind them that just as child napped twice only a short while ago he will transition gradually to an afternoon nap over time. Then make the move as soon as you can.

They may also be putting child to bed very early and want him to go home from daycare exhausted so he eats and goes to bed so they have evenings to themselves.

The fact they think they can make demands and control the daycare is the part to address more than that the actual time for the nap is too disruptive to the day for home daycare. In a daycare centre in the baby room there is more chance they will do this schedule as they like always having some of the kids asleep. I would be asking what is so important about that time frame that they think it needs to always be that and likely you will find what they are really asking for is that his schedule now be maintained and that is where you remind them that he is changing his schedule constantly anyways and then wish them a good day and keep iterviewing.