What difference does it make that your youngest daughter's new place to live "doesn't allow pets" if it's her support animal necessitated by her mental illness? The ADA and fair housing laws permit support animals even in housing that does not allow pets - as you already know.

There's no law that states how many animals may be classified as "support animals" for a single person, nor is there any law that says you can have more than one (although I understand that some people do).

If the cat doesn't live with you, even though you "own" it, it may be a hard sell that the cat is in any way an emotional support animal to you - other that the cat's needing a different home, you've not indicated that your needs have changed.