Awful behaviour when I'm not around

I have two five and a half year old boys in separate classes, half-day, in Senior Kindergarten (so it's their second year of school).
At home they're pretty well-behaved– they listen most of the time, they do fight sometimes and are pretty "hands-on" with each other in general, but don't often hurt each other.
At school, though, on the playground, I often get other kids coming up to me telling me they were pushed or hit by one of my sons (always the one I'm not currently watching.) I also had DS1's teacher tell me today he hit another student in class and he's been acting aggressive (hitting/pushing/kicking) on and off since school started. They went to a birthday party for a classmate this past weekend and DS1 said that DS2 hit another child at the party (the parents didn't say anything to us, and DS2 denies it, but I feel nowadays I can never be sure. Denying they hurt someone else is also something they're both starting to do, and while that may sometimes be the case, it's definitely not always the case.
When we see our kids hitting (or if we're told after the fact) we say "we don't hit", encourage them to apologize and make sure the other kid is ok, remove them from the situation (normally with a time out, but if it happens more than once we'll leave). We also encourage them to use their words, telling them what words they could use in various circumstances.
It seems they often (but not always) hit if they're frustrated. They'll also push/hit or otherwise act aggressively if someone acts aggressively towards them. And they also sometimes do it if they LIKE a kid (DS1 has been grabbing his friend's nose in class because he thinks "he's cute", but he does it hard enough to hurt his friend (I just found this out today)).
I am so frustrated. I feel like they are regressing socially (this level of roughness is new.) I feel like no one is going to want to play with either of them because they can't play nicely. I don't know how to handle this behaviour– if it happens when I'm around I can deal with it immediately, but so much of it happens when I'm not there.
They are smart kids, and can be so kind and good, but this new level of bad behaviour is really distressing, and I'm worried they're becoming kids that even I won't want to be around.
Has anyone experienced anything like this? And found some way of making things better? I'll be talking with both their teachers tomorrow, but beyond that I'm not sure what else to do.

 

I really don't know. My two can be a little rough with each other but not normally with other kids.