Just don't let him tell you no. You are the parent and the one in control of the situation.
Yikes!
It's his body, his bladder, his bowels.
This is merely an inconvenience to everyone else, but it is HIS body.
Thanks for all the wonderful advice and thoughts. We had a speech eval done in the summer, at that point they told me the best thing I could do is get him around other children.
During the week he is at home with my mother and his baby sister, that is why it is important to me that he gets to go to school. Most of the time he is stuck in the house, playing or watching TV. I know he enjoys getting outside and playing with the other kids.
This might be overly simplistic, and it's only based on what you wrote right there. But if they think his speech delay could be improved by being around others...why would it be around other children. I mean, if I'm going to teach a child to speak, I'd rather it be from adults, ya know? I wouldn't want someone learning from my son, who has a slight lisp and doesn't say L all the time, because of the way his teeth sit and that he's missing 3 (one accident with a new tooth and two extractions at 2.5 yo). I myself once picked up a stutter after spending the summer with my stepsister (who had a true stutter). It took probably 2 months for me to stop that; it was purely something I picked up from her, as I'd never stuttered before that.
And this is VERY simplistic, but it worked for my son and my cousin's son...Blues Clues. I spoke to and with my son ALL the time while at home, but he just wasn't interested in talking much. Then I came across Blues Clues, started watching it once or twice a day, and all of a sudden it was a language explosion. There was something about that male voice in the house during that day that did it. Every time we watched, he would pick up another word that Steve or Joe said on the show, and that wasn't normally used by me or DH, so he was truly learning from the show.
So if this is a very simple speech thing, I would ramp up on having adults around him speaking to and with and around him... (DS is watching Alvin and the Chipmunks right now, and I have met some kids who talk almost like them...my half sister was one of them until she was about 10, such a high tiny voice who talked fast...so it's kind of a funny thing to have one while talking about this).
And all that said...another cousin of mine did the weekend potty training with her son and I guess it worked. A friend of mine was up against the same daycare thing as you are, and her sister in law couldn't watch her son anymore, so over the summer they took away every last one of his toys until the very last one...and he finally gave in. It was a hard, hard summer for all of them (and it's very possible he would have learned the potty on his own by the end of the summer, without the trauma and yelling and losing toys).
Lastly, consider switching to cloth. We used cloth, and DS started learning about the potty at 18 months. I was the one that slowed him down b/c it made me so nervous! He actually spent nights dry first, but that's b/c we have a family bed and I FINALLY learned that when he got squirmy it was b/c he had to pee, so I would put him on the potty, pull his dipe back up, and he would sleep the rest of the night (mostly). A year after he started, I did the final wash and dry of the dipes and put them away. Cloth can be most helpful for kids to not want to spend years wearing diapers!