I agree with everyone else that that doesn't sound very age-appropriate. Three is far to early to start criticizing hand-writing on any level at all. If it was my kid I'd definitely be looking at a new program. I feel strongly that a preschool teacher should be a kind presence that is supportive and nurturing more than anything else.
It can be really hard to get the perfect read on a school or even to predict what it is your kid will 'need'. Around here there weren't any strictly play-based options that were close enough for us to attend but there were a ton of church-based preschools that all seemed to use the same general curriculum. I ended up putting my son (3.5) where he is now because when we visited all the kids looked like they were having a good time, the teachers were very sweet and they talked to my son like he was a person to a larger extent than other schools. I've really enjoyed it for him so far, and I'm happy with the decision. He does do some writing work but it seems to be pretty rare and is just tracing some letters. They have a letter of the week that they talk about and then they decorate the letter with something. There doesn't seem to be much pressure to do much of anything other than stay somewhat in line and in their seats. I don't think he's learning much academic but has plenty of behavior to work on, ha.
I'm sorry you guys are having a rough experience and I hope you find a school that's a good fit soon!
