Your D9 will be one happy girl. And so will D6 if you make it special.
As for outings with your H, only you know your comfort level - you say you don't want to - there in lies a clue. But you are wise to always do what is best for the kids. There should not be any misconception about where it is going, though. How does your H feel?
I do NOT have any outings with my ex. But our split was VERY nasty and I don't have much communication of any type with him anymore. As well, our kids are older, so that's different.