It sounds like a difficult situation to get involved in. On the one hand, you say the kids are having a hard time with the divorce. You've been dating a year and a half but only started interacting with the kids recently. It's not a surprise that they are not ready to include you in some activities & given they are in therapy, having such a hard time adjusting... it would be sensitive for you to bow out & let him take just his kids to the game. You weren't going to go to begin with. If they were free tickets, why make an issue of it. Is if "fair"? Not really but it kinda comes with the territory of getting involved with someone that has kids.

On the other hand, I would agree that the dad needs to maintain control as the adult to keep kids from manipulating... and I might even go as far as admitting it's possible that the anxiety attacks and crying or clingy behavior could be manipulation. BUT, this guy has been dating you for quite a while before including his kids and he may not have prepared them for this new situation, he may feel guilty & they may have been getting away with manipulating him for a long time. They are not going to welcome someone that might change things.

I get it if you're feelings were hurt. A few years ago, I thought it would be nice to take SD and buy tickets for a fair on Father's day. It was to be a surprise for DH and I bought all the tickets (SD was with me). We got to the fair, rode rides together & played games but halfway through the day, she took her dad aside and started crying. He was astounded and asked what's wrong. She tells him (loud enough for me to hear) "I didn't know Ima was going to be here, I wanted it to be just you and me!". Of course I was hurt & angry. She was with me when I bought the tickets & when we made the plans to go & when we got in the car & when we spent the first half of the day there together, having fun or so I thought. Thinking back on it now... maybe I should have gone home & let them have the rest of the day. I don't think it would have made much difference in the way things have ultimately turned out, which is now having an almost 13 year old that ignores me like I don't exist. She never wanted her dad to be with anyone, she will probably never accept that he's with me & it's uncomfortable (at best) to live on a day to day basis with her.

If you are already feeling it has disaster written all over it AND he has a crazy ex.... well, that's more insight than I had before I said "I do".

I answered this on your other thread but I'll repost my answer in case you didn't see it:
"I have seen quite a few instances where my BF will say to stop a behavior in excess of 5-6 times, kids ignore him, and he does nothing OR worse if the cry or pout he will placate them with a reward (candy, toy, etc). I think he is setting up for failure and worse behavior in the future. "
I think you're quite right. IMO the kids have meltdowns because they have learned that that is what works for them, perhaps not consciously but it is what they have been conditioned to do. Already your boyfriend is reaping the whirlwind he has sown. If my DD had tried to set the rules I would have reminded her that the family is not a democracy and parental veto overrides all. Some latitude in decision making is a good learning experience for kids but in that particular situation it wasn't appropriate IMO, except for the son to decline to attend.
So, since the girl declined, is Dad going to take her on a special treat too? That would be the fair thing to do since he has set it up for the son.
I dunno. If you've been dating for 18 months (and presumably the divorce happened before that) and the kids still have meltdowns, perhaps it's time to reassess where this relationship is going.
Granted you've only been interacting with the kids for 2 1/2 months but I would have thought that 18 months post-divorce they would be more settled than they are. Since they're not, it looks like it's going to be a long, slow haul and you may never get there. Are you ready for that?