I am pleased you have the mothering instinct that you somehow need to protect your daughter. It is bang on.
When he criticises her behaviour say 'please don't say that about dd', 'please don't compare my dd to your son, all children are different'
'Actually I find your comments regarding her behaviour quite hurtful'
His behaviour is IMO quite abusive, he is expecting your lovely dd to behave in a way that is totally inappropriate to her age. She can't act the way he wants because she's only two. Still a baby in lots of ways, still needs her mummy, still needs nurturing etc.
He doesn't like her demanding your time and attention because he wants it all and therefore tries to make out that she is a bad child.
Please don't listen to him. Don't leave him alone with her either.
Remember this: we have a choice who we bring into our childrens life, they don't. They just have to put up with it.
That's why it's vital that is as mums make good choices as to who are role models for our children when starting new relationships.
Your new mantra: please don't say nasty things about my dd.
Him: blah blah
You: please don't say nasty things about my daughter.
Repeat. Repeat.
If you need to keep repeating then I'm afraid you need to consider a future that doesn't involve him.
Good luck.