Could the fact that he's only there mid-week be contributing? He is at home for 4 day stretches, Friday to Monday, so if they're doing something different or coddling him, then it's going to take him longer to really realize that naptime at daycare is different. Maybe ask them to write down exactly what happens at naptime at home? Then either ask them if they could change what they are doing to be more in line with what you do, to give him consistency. If they are lying down with him or giving him a bottle to get him to sleep, then that would explain why he's fighting naptime with you - he's waiting for that, and 4 days at home getting it is a long enough time for him to forget what it's like at daycare, and then after 3 days with you, just when he might be getting the hang of things, it's 4 more days at home with whatever they might be doing.

Might be worth looking at, if you can get them on board with having naptime being the same thing every day, it won't take nearly as long for him to get used to what is expected (hopefully!)

Good luck!