The problem is of your own making.
There is and was nothing stopping you from making your own plan and do a cultural activity, with DH and DD, and then come back late afternoon so DD can have a swim with her mates. That way everyone would have been happy?
We just did a holiday like this, and ended up wasting one day as we were supposed to all go out and it ended up not happening due to friends,faffing. The next day, we booked something. Told friends that's what we were doing, and what the website was if they wanted to book too.
The day after, DH and I went out and DS wanted to stay by pool, we checked with our friends if they were happy with that, they were.
No drama. So what if you like different things.
Your mistake was thinking you should do everything as a group, and that they should join you on a cultural activity they were not interested in.
At 6, you could have easily told DD:"we are going out, you can play in the pool when we come back" and just go.
The fact that you are afraid to "upset" DD, and cannot tell her what to do, is a problem with your parenting, not your friends' parenting.
Shame it marred to holiday experience for you, but it could have been so easily avoided...