My ex has moved farther away since our divorce. Isn't he/she responsible for more of the transportation since I wasn't the one that moved?
Possibly, but don't count on it. The courts generally like to see an equitable division of transportation-related responsibilities, but if your ex moved (with the children) far enough away so that transportation becomes a significant issue, they may order that the party who moved to be responsible for more of the transportation costs or distance.
There are few, if any, restrictions on non-custodial parents who chose to move, although the court will typically make them responsible for at least half of the transportation costs if their move takes them farther away from the children.