foster and maintain a relationship between the child and her mother over those three years abroad? You realize, of course, that the burden would likely be upon you to provide transportation both ways, yes? Can you afford that expense, on top of the tuition (yes, you are likely to be 100% responsible for that, too)? It is also not impossible that you will be required to post a (significant) bond should the child not visit her mother as ordered.
Honestly? I cannot fault Mom for fighting this plan, and it would surprise me greatly if a court agreed to allow the child to do this. If you are concerned with her schooling (and her brother's poor performance may or may not be relevant - you would have to prove that it was Mom's actions and behavior that caused his failure), why not simply look at a change in custody, a change in school, or maybe... get further involved in her schooling yourself?
While I'm a huge fan of gaining an "international experience", three years is pushing that envelope, IMO.