OP, I don't know what the consequences for you are if you cancel this week's appointment if you don't have a sitter, but that's what I'd be inclined to do in future. My DD has autism, and there's no way I could have taken her to that kind of environment at that age. Of course, I had to try it once to know that it would be a disaster.
I think what was said was pretty insulting. If your teacher didn't know about the autism, it's entirely likely that she believed DS to be a regular 3 year old having a tantrum.
How is it not insulting to tell a parent of an apparently normal child that 'they're in over their head' when they're dealing with what looks like misbehaviour? I don't think there's any way that can be interpreted as a helpful statement. To me, it sounds just like, 'You're obviously incompetent'.
And dealing with autistic meltdowns, or even normal tantrums of an autistic child can make you look pretty incompetent at times, because you have to do things like pin the child down, or give them the things they're screaming for,or sing the same song 700 times while sitting in the middle of the shopping centre etc. All of which make you look like you can't do the normal things that parents of tantruming three-year-olds do to get their kids to calm down. But being told you're in over your head in that situation when you're doing the exact thing that the child needs is pretty insulting, and depressing.
OP, I completely get why you're insulted, and to have it come right on the heals of a diagnosis when you're trying to come to terms with all that means is really shattering. But, to be honest, I think I'd let it go, especially if this teacher has been good for you otherwise. Maybe let her know the info about the diagnosis and what treatments will be required at some stage, if you would like to.
Best wishes in finding the help that you all need.