I really don't have any ideas as it seems that you need your son to be there because you are at work. But I wanted to let you know that this is normal, at least in our house ;)
When my son started preschool at 3yr old he loved it after a couple of rough drop offs. The teachers kept urging me to leave him for a full day instead of picking him up before nap, they insisted that he was ready for it and I would get a longer break (I had a new baby at home). My instinct told me he wasn't ready as he hadn't napped in over a year, but I left him because he said he WANTED to stay for nap because most of the other kids did. I should have listened to my gut.
After napping there once he was totally freaked out and HATED school, screaming in the car on the way and hanging on the fence when I dropped him off. He only went three days a week but all seven days a week he would ask in the morning "do I have to go to school today?" I even had started picking him up before nap again, and assured him daily that he didn't have to sleep at school anymore, but he was just ruined. He didn't ever seem to recover until we switched schools (for financial reasons) where there was no nap. Once he was told that the new school didn't have a nap time, he went happily!
Maybe your nanny can pick him up after lunch? I don't know if that's in your budget to pay her five days a week as well as paying for school for both kids, but it may help.