I personally don't get angry about these things, or at least try not to let the parents feel my frustration. I also need my break time but I try not to sweat on these things. I can understand your frustration as we all go through similar situations that are annoying. But i think sometimes we need to stay positive and try not to let these things get to us. Unless it's all the time then I would definitely say no.
I had one parent ask the same thing, she had a doctors appointment for dcg during nap time, I personally don't think It's a big deal. Sometimes plans are made because of other circumstances that are beyond their control. I don't think I can tell the parent not to come. I think its ok to ask if it's possible to wait but if they don't then they don't. I put her to sleep a bit earlier and went into the room 15 minutes before pickup and quietly picked her up. None of the kids woke up and mom was here right on time. I have my kids fully dressed and ready to go so pick up is always quick. Or do like bright sparks suggested and swith rooms for that one day. But i think your dck should be fine.
Good luck working this out with the parents, I'm sure everything will work out![]()