The 80 day thing may have to do with child support. Have you researched your state's child support formula? In some states it is based purely on income, in others it is based on a combination of custodial nights and income. I think he is getting advice somewhere. It has nothing to do with another man. I know you have said a percentage, but you need to make sure there isn't a time factor also figured in.
You want to end up with an agreement that leaves no DOUBT that you are the primary parent.
He seems obsessed with you meeting a new man. I suspect that this is part of his financial strategy. He [censored] big time.
80 days would give him about 20-25% custody. That is a lot (in my opinion) for someone not even living in the same country.)
If you are divorced in the US, whatever court divorces you will have jurisdiction. I am not sure what good a lawyer from your new country would do. Whatever, make sure he is the one who pays for it.
You may consider storing the passports with a trusted friend or hide them really well.
What happens if you refuse to go to Europe? How does that impact his plans?