Abba: Al Pi Halacha an ex-wife is not entitled to alimony. If she forces him to pay monthly alimony via a non-Jewish court ruling kneged halacha then she’s a thief. A wife who stole from her husband is not supposed to be given a Get (even if she would otherwise be entitled to it) until she pays him back. See Rav Moshe Shternbuch, Rav Elyashiv’s and others teshuva on this subject.
As far as her wages and earnings, they belong to the husband until she makes a formal declaration to him that she discharges him from being obligated to support her. Any earnings of hers after that declaration belong to her. And he’s no longer obligated to support her.
Child support is the husband’s obligation Al Pi Halacha up to a certain age. (It is less than 18.) But he’s not halachicly obligated to give the child support money to his ex-wife. He can choose to spend it on his children directly.
Using any non-Jewish court for rulings on child support, alimony, assets separation (halachicly virtually all martial assets belong to the husband unless the wife owned it prior to their marriage) or any other disputed matter is strictly against Halacha. ALL disputes MUST be adjudicated in Bais Din only. If any party utilizes arkaos (secular court) then they lose any rights they otherwise would have against the other party.