There IS a middle way.
We treat our AP just as I was treated when I was an AP - if she is with us, she gets what the kids get (movie ticket, ice cream, popcorn, lunch, a bottle of water, a ferris wheel ride etc.) but that doesn't mean that there aren't things we do alone with the kids. She is cordially invited to everything but all our APs have said no to things because they didn't care for them, had other plans or were just happy to have the house to themselves for (half) a day.
Yes, all come to the amusement park at least once (not the mouse), so far all have gone back alone with friends because it's much more fun to go on the rides you want to go on and not the rides the kids can go on. We had one whom we just gave a ride to the park (and back) who met friends there, we paid her ticket (she was stellar, she deserved it) but she was on her own during the day.
They all go to the fair with us once, some more than once (we have three local fairs each year) and all are treated for dinner (because that is what is dinner that night - bratwurst, fries, noodles, churros, crepes, a soft drink), they get a ferris wheel ride with the whole family and we will wait for them if they want to go on another ride but it comes out of their pocket (same for the kids, they get one ride, additional rides are paid with their pocket money). Saturday markets, we go every other week, sometimes they join us (as market includes breakfast), sometimes they don't. Some join us for hiking on Sundays and if everybody gets ice cream, of course they get ice cream... but if they don't enjoy hiking, they don't have to come. Some go to church with dad and the kids, some are gone most of the weekend, some are home and enjoy the peace and quiet of an empty house with me. If we decide to go to the zoo and they come of course I pay for the zoo and their lunch and ice cream. They are adults in that they get to pick, the kids are told (and mommy makes the rules) but if they chose to come I cover the cost. If I don't want to cover the cost I tell them in advance and tell them that I am sorry I can't take them. That has so far happened once, was grandma's Christmas present and was actually a weekend without the kids (who spend the time with their aunt and uncle).
Currently our vacations aren't too exciting. They are invited, they usually pass. They can come to visit grandma but all they get is a couch (grandma has one guest room with one bed, mommy and daddy get it, tough luck on everybody else, I am too old to sleep on the floor, the kids can, AP can have the couch, I assume AP could snuggle up between us as the little one does but I am sure they all prefer the couch), some have joined us and some passed. We usually rent vacation homes, we ask her if she wants to come when we book it, if she says yes we make sure there is room for her, if she says no we don't mind. A week at the beach in the middle of nowhere isn't too exciting for a 20 year old and we understand, we have had one who was happy to come and spend most of the day at the beach, reading and relaxing. We did count it as a work week as she was supposed to help in the mornings and was an extra set of hands by just being around (and there was nowhere to go).
When our kids are old enough (16+) they will get choices, just as the AP has choices. Right now the kids don't because they can't, tough luck. We can't leave them alone yet so they have to come. Giving the AP space also makes space for the nuclear family alone (NO au pair has joined us for every single little family activity) and for us as a couple alone (we do date nights with a babysitter, AP is off and we are off, but we don't spend that time together).