If he doens't mind being wet, then he is too young for potty training. Relax about it and put him in diapers if he is not trained. Give it 3-6 months and try again. No day care providers in their right minds would expect a 2 year old ot be potty trained NOR should they expect he will cooperate about wanting to use the potty (and telling them he has to go). He CAN tell them, he just isn't going to all the time.
I have found most moms start to potty train at age 2 and get really excited becasue their child goes and shows and interest. But most don't have success until closer to age three if not after. Kids have to have control AND desire. And if he doesn't, just wait. You are making your life a lot more stressful.
My daughter day AND night potty trained around 34 months within a week with only 1-2 accidents. Great, right? No! Those first few months were awful "Do you have to go? Are you sure? Really? Okay, pull down your pants... no pull them down all the way. Now sit down. No, don't touch that. Don't touch that either. Are you going? Well, stop singing and hurry up. Don't play with the toilet paper. Now wipe. No, wipe better. No not like that. Okay get down. Pull up your pants. Please pull them up NOW" And that isn't even including hand washing!!! Wait until he is ready and able and WILLING!
PS - All tha tbeing said, the method that worked for me and many friends is what I call "Naked Weekend" Stay home with no clothes, make a big deal out of it, giv elots of juice, and let him figure out tha tit is hard to play where you pee, especially if you have to stopa nd clean up your own accidents :) My guess is, he is still too young, but when he is ready, that might do the trick.