I'm sure it's not the opinion that you want to hear, but from a practical perspective it sounds like the kids will be in a better situation with their dad. They'll have one long-distance parent either way, and it sounds like if they move with him they'll be in better schools with better family income.
How stable is the relationship with the girlfriend? That might give me a little pause, but if it's a good, stable relationship that looks like it's headed toward permanency I think that would put the seal on it for me.
So overall I think if it were me, I'd put my feelings aside, hope to get as much time with them as I could but let them go live with their dad.
Maybe get the agreement on visits in writing (as in , part of a custody/visitation court order), and if he's making good money he should be able to commit to financing the travel to make sure the visits happen.