R.M.
Hello L.,
I've potty trained quite a few children when I was a Nanny, and it's a tough time. Children around 3 start becoming more strong willed and independent, which is great, except when you want them to do something.
At preschool, your son wants to impress his peers, so he goes easily and willingly. At home, he is digging in his heals, I would guess, because you ask him to go potty at a specific time.
I suggest you take yourself out of the equation as much as possible. Give your son a watch with a timer. Set the timer for every 45-60 minutes, and let your son know when his watch beeps, he should try to go potty. You could even give him a time window, but allowing it to be his choice.
If you think he is just not trying, it's a good idea make him clean-up his mess himself. Cause & Effect, if you don't use the potty, you must mop the floor & do your laundry, but be sure it's cause & effect, not punishment. Punishing for accidents can cause backwards steps.
Good Luck!
R. Magby