Hello T.,
i didn't catch how old your child was, and this may have an impact on how long it will take, however,
I am also a daycare provider in my home, I also use the pack and play type beds, they will eventually adujust. There is no need to wory The Idea of the "baby bed" as we like to cll it, is to keep them safe, and kept from continually getting up if refusing to sleep.
A tired child will sometimes "fight" sleep, and in the baby bed, they usually settle down eventually. it really only takes a short amount of time before they understand this is the way it is done. I use these throughout my home, and I have had my share of disagreeable children. They will learn this is the sleeping place, if your provider is consistant.
I even have children in my home who ONLY nap for me, their parents love it. They are so used to the routine, it just comes naturally.
Good luck and hang in there.