Because divorce brings out the worst in people and add Alcoholism to that mix = whatcha got.
My impression is that he did want you to move back. This was negated early in the divorce proceedings because you are a European citizen; therefore, the Courts had no jurisdiction to force you, or the children, to return. Also I believe he initially petitioned for full custody of the children and lost that battle.
Clearly this set up was something that had been going on before the divorce - and you were ok with it. You STBXAH has never "lived" in the Country you moved to. Being a trans-Atlantic family is a decision you participated in.
Tell me, if he called tomorrow and said please move back so I can see the Children more would you? He is what he is. The distance seems to have been to all your benefit given his history of physical/mental abuse.
You don't' need his permission to move back. If you feel the children should see him more move. It would definitely alleviate a lot of the financial injuries you have sustained living in the place you do which you have stated is extremely expensive.
As far as the rest its just fantasy land - why, why, why why. Why can't he be like this man who can't live without his kids, why can't he play fair, why can't he stop using your children as a moving target? Why can't he just settle this divorce and move on? Why must everything be a fight? Why can't you guys just talk pleasantly and do what's best for the kids?
As KTF said - because he is a deep level alcoholic, and normal behaviors/emotions/feelings aren't possible.