Is the European Court's divorce ruling considered a legitimate divorce [under Islamic law]? And what is the ruling concerning the "suspended" wife whom her husband bargains with over child custody in exchange for her divorce?

A wife does not leave her husband's عصمة (bond of marriage) except through a divorce issued by him or by a legitimate شرعي judge. A divorce issued by a civil court is not enforceable. It is permissible to waive custody of children in exchange for a divorce. A wife is not allowed to seek divorce except for a legitimate شرعي excuse, and her husband marrying another woman is not a permissible excuse for that. It is advised for the husband to divorce his wife if she insists on it, to avoid her remaining in a state of being "like a woman left in suspense" (معلقة), and he has the right to claim his rights from her regarding child custody or compensation if that is in his interest.