Well, actually, you don't "move" the server (if you can avoid it), because of precisely the problems you're experiencing.
The Microsoft recommendation is to migrate the RDS role from the existing server to a new server you've prepared in the other domain/forest.
Following the link, you can see that it's not a trivial procedure, and varies greatly depending on your exact configuration. If I were in your shoes, I would probably try to put the RDS server back (join it to the old domain) and step through the migration
procedure in the documentation I linked. If joining the server back to the old domain doesn't fix your issues (and it might not), then I think your best bet is to restore from backups, and try the migration procedure.
Oh, and try to sort your admins out. Just joining a server to a different domain does not strike me as the actions of someone who knows what they're doing. I could see trying it myself, but only after backing everything up, and preparing to quickly revert to
a backup/snapshot in the expected case that it didn't work.
