He is being unreasonable, no you don't have to go with him and chat nicely, yes if you see him you must be polite for the childrens sake but you are getting divorced. He is hoping you will cave or at worst show his kids how unreasonable you are (which is not true).
This situation with your DD, was me as a child. My Mum was honest and accommodating with my Dad and when I went to Dads he guilt tripped us. As a child its difficult and I loved my Dad but he was asking me to do and say things I wasn't happy with and so I avoided going as I didn't want him to be disappointed with me....that created problems with me and Dad and my siblings who wanted to go to Dads and he pulled the "if she doesn't come, you can't come routine! Me and my siblings were fine when we were with Mum, but the arguments all revolved around Dad. He loved us and felt he was being short changed by the divorce, even though it was his behaviour that was the catalyst for it. He very much lacked self awareness. As an adult I can rationalise that he very much loved us, but he was dysfunctional and did not realise his issues and blamed Mum. Don't get me wrong, part of the issue was that this went on for so long, because Mum had facilitated his behaviour by keeping quiet to keep the peace - its a vicious circle. But ultimately if someone repeatedly does something wrong and nothing is said, it does become a big unbelievable shock when they eventually they have to face it, as no-one has said anything before. So stand firm lady!
What I will say I have picked up though, is that he seems to want to spend a lot of time on activities for his son, which may unintentionally alienate his daughter further.
You are one hundred percent doing the right thing. The fact you are thinking you should stay with him for the kids sake shows your love for them, but its wrong. Do you really want your kids to grow up in that environment, thinking that this is how adults behave and what relationships are?
Sending you big hugs and please continue the updates, as I am heavily invested in this now.🥰