How does he act when he's home with you taking the shorter naps? If he's fine, he may be ready to go to one nap a day. He might be sleeping longer for the babysitter since he plays harder and has more stimulation while he's there. That kind of hard play would be hard to replicate at home.
If he seems to need more sleep, you might try getting him to sleep longer at naps the same way you got him to sleep through the night. I know our older on when through a stage where he woke up, but really wasn't ready to get up. It was tough to get through, but I just didn't let him get up. Interpretted that means a lot of crying for about a week.
I hope you get something that helps!