A lot of kids have trouble figuring out the potty in another situation, whether it's preschool or someone else's house, a store or restaurant, etc. There are distractions, there is a schedule (circle time, art time, etc.) and they just don't always think to break that schedule to go to a different bathroom. Moreover, a lot of potty-trained kids have accidents when they sleep. My child was like yours in that he took 2-3 hour naps, actually well past the age of 4, so he really had a deep sleep during the early afternoon. Even "daytime" potty-trained kids often do not wake up from that.
So the school put him in a pull up because he's NOT fully potty-trained. Sounds like a reasonable decision, frankly. They put the underwear on over the pull up either to keep your child feeling that he was wearing underwear, or to prevent the underwear from being lost. Either way, not a bad decision. And they felt it was more important for him to have a good rest and not wake up wet.
I'm sure the director's "shock" was a natural reaction to a parent's complaint, not that she thinks pull ups are a terrible idea. Once she checked with the teachers who are dealing with your son every day, she felt it was a reasonable decision. I think you'd be amazed at how difficult it is in preschool to get a bunch of kids to go potty when they don't think they have to, when they'd rather be playing, or when they're starting to get tired and need a nap.
It may just be necessary for your child to develop a little more. You may also want to re-think the idea of having your MIL take him out before nap - if she takes him out, he misses the routine of school and the habit of going potty before nap. Even if you tell him at 8 AM that he has to go potty before naptime, he's not going to remember that at 8:10, let alone at 1 PM.
I wonder if you are so opposed to pull ups that you take it as a real insult to your parenting that someone else would disagree and do things differently? I can't imagine being so incredibly angry that you would pull your child from the program. That seems way over the top. It really seems like you consider their different style to be an affront to YOU, rather than a hugely horrible decision for your child.
If you are going to pull your child from a school every time you disagree with a teacher, you're going to have a very, very long road through your child's education. The disruption alone will be far worse for him than wearing a pull up. He will lose socialization, stimulation, friends, skill development, and many other advances - just because he's not fully potty trained at 3.
Maybe they should have discussed it with you, but if you've had any conversations with them on this issue and they felt you were inflexible, maybe they avoided it. Or, perhaps they just didn't think this was the big deal that you think it is. A school can't possibly keep track of every parent's strong feelings on a particular issue. For me, if the kid is safe and having a decent time, I'd let these things go. If he's being fed something he's allergic to, or misplaced on the playground, or being bitten by another kid, then I'd complain. But a pull up? No way - I'd look at the big picture and give him some continuity and structure, and just let him be a little boy.