Your son is missing his father - not necessarily the person his father IS, but certainly the person your son wishes his father had been. He feels rejected by his father, so having his father "want" him now feels kind of nice and reassuring.
Sounds like his father has no clue what kids need - consistency, a feeling of belonging, and so on. The wedding, the trip and the long absences tell a pretty sad story. And now your ex has put your son in the role of being the messenger. I'm not sure if the "come live with me" invitation is about reducing child support, or about making up for being a bad dad, or about control.
I agree that children should not have the job of making their parents happy. You need to make a decision that is best for your son, but which doesn't drive your son toward his father any further. Can you agree on an extended visit during the summer? Unless you think he wouldn't be safe there, it might be very telling for your son to be in his father's house for, say, 2 or 3 weeks, and then find that it's not so rosy, Dad is irrational and angry, is off at work and the teen is left home with the stepmother and her children, and so on. I think you can tell your son that the courts decided this based on all the evidence and in an objective manner, but that you also don't want to keep him from his father, so how about a visit to meet those father-son needs. My guess is your ex cannot hold it together for a long period of time, and that will be quite telling for your son to be in that environment. It's important that you not say, "Okay, go for a long visit and then we'll see if you still want to live with Dad." That sets it up that a) you don't have a final say and b) Dad can manipulate the son enough to make things happen.
People can change, but it doesn't sound like your ex has been proven to be a different person. If he were, he would have discussed this with YOU and not made the son the messenger. I'd highlight that to your son, and make your decision about what's best for him, not just that you are protecting him from heartache. It's also not up to your ex - his wife and her kids are affected too. Does your ex have a room for his son (and his other kids)? How well does he integrate his "new" family with his "old" family? Who has to adjust to whom?
I think it's awful that your ex twisted your daughter's arm like that. I think your son should spend the next year seeing how dedicated his father is to all 3 kids' activities (games, graduations, proms, parent-teacher conferences, and everything else). THAT'S what it means to be a parent - not just be Mr. Weekend Good Time. But I think you MUST acknowledge your son's desire to have a father, and hold back from saying too much of what you believe his father's shortcomings to be. You don't want your son making his decision based on taking care of you or his siblings either. That's just more of the manipulation or undue influence he's already feeling. At his age, he's trying to be a man and subjugate his own feelings, to do for someone else. Try to help him through that in as healthy a way as possible.
I sympathize - kids in our family went through a lot of guilt trying to take care of the needy parent who manipulated, and it affected their whole life and the choices they made in spouses. Not a good situation. Good luck!