And H sounds like a d*ck. Demands, demands. I am sure you will come up with the appropriate response along with your lawyer. In my jurisdiction, if custody isn't agreed to be "shared", then the only option is sole custody (separate from visititation). One S is an adult, so does not count (again, support is a separate issue) and your other is over 12. Can't see a Court forcing him to go with dad, if he does not want to.
The only thing that concerned me about what you said above was: "The mortgage is in good standing so it won't go into foreclosure and I highly doubt a judge will force me to sell it with a minor child in residence when I've secured a mortgage on the basis of money from h I'm entitled to."
WR, does this mean you will depend on the support your H is supposed to give you to continue to mortgage? Have you actually secured the refinance? Different jurisdictions, but mine does not consider support as part of the ability to pay. Yours may. It's too risky, you see. More often than not, support is simply not paid or cannot be counted on. You would be very wise not to count on it overmuch. there are limits to remedies available when H does not pay.
I am sure your L will go through all this with you. I don't at all mean to be gloom and doom, I am just familiar with what happens when people rely on spousal or child support only to never see a dime from it.
Otherwise, you sound like you are in a good place mentally and I am glad for that. Life does go on, doesn't it?