I was in your shoes exactly when my son was 36 months. I never use pull ups except when we left the house, underwear in the house. My pediatrician told me not to push it, or I would make it worse. He would still resist and then hate going and then if you try later he will still associate it negatively. Then I researched it more and the average boy trains between 3 and 4 years old. So, I figured that I shouldn't push it. So, we tried for a week and if he was still having a lot of accidents, we would stop. So, we stopped and tried again when he was 3.5 years old. That worked like a charm. The first 2 days were non stop accidents, but then I think he realized that I wasn't giving up and on the 3rd day he started going all the time on the potty. I also made him a "potty chart". He got to put a sticker up for each time he went on the potty. Then, once he reached a certain number of stickers, he got a prize. That made him feel like he had some control. Also, every time he went on the potty without an accident I gave him TONS of positive praise (and got to call daddy and grandma to tell them). I also tried to focus a lot on when he did anything good (gave him tons of praise) so he would feel really good about himself. I used pull ups when we left the house for a week, then I dropped those as well.
I used to be one of those moms that believed that you could force a kid to potty train. Now, having been through it, I realize you can't force them to potty train. They need to want to do it themselves. So, you can try to make him go, but it sounds like he isn't ready. Save yourself and your caregiver the stress and went a few more months. He will get it one day, and then you will be glad that you didn't go through a nightmare of a time trying to train him. Let it happen naturally. Good luck!