SR- I might be missing something, but is there a reason you can't just take D camping with the 2 of you only? Form a "Daddy" activity that's a new special ritual for you two? Up here there are places that even have tent cabins so you don't have to have equipment, etc.
One thing that offers me activities is my moms group. Now I know, it's called a "moms" group, but maybe there's a dad's group or even a single parent group around? We have a mom's night out once a month and playdates, and since I've gotten to know some moms, D gets invited to b-day parties on the weekends now, etc. I don't know if that's your kind of thing, but you know, the distraction is nice on those long weekends! I also know the bored feeling when they want you to play with them, the same thing over and over LOL. And I feel guilty for feeling bored, but lately I've asked a couple moms of D's friends from preschool to meet at park on Sat mornings. It's amazing how the kids entertain each other so you get a little break mentally and don't have to entertain them. To me it feels like downtime! I didn't know these parents before- just kept talking to them at school at pickup and gradually got to know them, etc. Or is your daughter interested in something like Brownies that you could do togther?
Another ritual I started lately is taking my D to the library every Saturday morning. She loves books, it's free, and it's a new special "mommy" activity that she looks forward to every week. Maybe there are some things you guys can start doing that feel special that she'll look forward to when she spends time with you?
When the men on the chessboard Get up and tell you where to go; And you've just had some kind of mushroom And your mind is moving slow; Go ask Alice... I think she'll know.
