Your son is typical for many kids his age, in that he wants more "grown-up" privileges with zero understanding of grown-up responsibilities. Sure, he wants his friends because he's 12 and it's not "cool" to hang out with (let alone have fun with) Mom and younger siblings. But he a) thinks you're made of money and b) doesn't understand anything about the manners of issuing and accepting invitations.
Time for you to stop being the fun mom who feels some obligation to give in to the kids no matter how unreasonable their demands. Time for your son to no longer invite kids without your permission. Time for you to stop taking kids who aren't invited by you.
It would be nice if other parents took your son, but they either don't have the money and they aren't issuing those invitations, or maybe your son's lack of manners and his sense of entitlement make him an unwelcome guest. If he doesn't appreciate what you do and what you spend, it's likely that he doesn't express gratitude or appreciation to the other kids' parents. If he were to go with them, would he be truly appreciative, or would he just say a perfunctory "thanks"? Where they to buy him an admission ticket, would he also asking for fries and sodas and souvenirs? Does he even have a lot of friends, or are they just coming with him because they get a free day at the amusement park?
I think it's time for you to find much less expensive activities, give your kids real chores so they understand the value of a dollar, and stop being blackmailed by a child who goes behind your back. In a few years, that kid is going to want a learner's permit and access to an automobile, and he needs to know that these things cost money. He's 12. He can earn money by weeding neighbors' gardens and pulling their crabgrass, mowing lawns, walking dogs and caring for cats/guinea pigs during vacations. If he's not doing laundry, he needs to learn. Younger kids can do this too. They should be getting all the gear ready for trips to the beach or pool, helping to make lunches and clean out used/dirty lunch boxes, and more. They are family members, not entitled celebrities. Your job is to give them the life skills so they can go out on their own, and you can't start that at 17.
There have to be consequences and responsibilities: we don't buy expensive snacks when we can make our own (buy a big pack and divide them up into reusable containers), we don't go to the amusement park when we spent our budget on the beach trip, we don't play all day when there's a house to run.
And where is it written that kids should never be disappointed? We don't always get what we want, and learning to cope is a major life skill. Kids who are entitled and never have to "make do" don't actually do very well in life.