Heath, you are obligated by halacha to give them a Jewish education. That doesn’t mean a Yeshiva education. That means you should apply for joint custody and whenever you are granted time with them, infuse them with chinuch. And chinuch doesn’t mean necessarily sitting a learning inside – it could mean anything from basics like Jewish thought/philosophy to how to make a bracha.
And yes, you are obligated to feed your children. L’halacha. Why would you want them to starve??
Reasonable accomodation doesn’t mean having to overturn everything to accomodate you if they can. It means reasonable. Like my friend who trades her saturday shifts with a Catholic woman for her sunday shifts. She gets Shabbos off, her coworker gets Sunday off. It works well for each of them.
As to two men – they can’t make a legal contract? How many business men do you know? How is a marriage contract (in American law) really different from a business contract?