J.V.
Sounds like you son is just a few steps away from being trained. It will take a few weeks to learn to go from bare bottomed to undies or trainers, and then it takes some time for them to really learn timing. It also sounds like your son still has some bladder control to develop, since they take kids at daycare to the potty often enough that most kids can hold it between potty trips.
I say just relax, keep on putting him in his trainers, don't make a big deal out of accidents (oh, did you go in your pants? I'm sorry, maybe next time we will get to the potty in time. If you feel pressure here, yell "mommy potty!"), and hang tight. There is sooo much to learn to be fully potty trained (control, then the ability to hold it, then timing). When he is at a 90% success rate in trainers, then buy him "special undies." Till then, no undies, just trainers. I found what motivated my kids with special undies. It was Elmo undies for my daughter. Thomas with my son. With both, they night trained a few weeks after going into their special undies during the day because they wanted to wear their undies to bed. (Full disclosure: I also moved them into cloth diapers at night when they moved into undies during the day and I know this contributed as well. Also of import, they were both under 2, so power struggles weren't an issue yet.)
A few other things: 2 and 3 year old are very distracted, so expect accidents even after days upon days of no accidents. They can also have accidents when totally melting down as they lose all control.