Is it permissible to open a second mosque in the same city—given that there is already a first mosque that is being subjected to theft by its caretakers, and they refuse to relinquish its management—which may lead to the closure of the first mosque due to lack of funding?

If funding the old mosque leads to embezzlement, you must stop that corruption by any available means. And there is no religious objection to building another mosque and funding it. We advise informing the aforementioned official first, before proceeding with his dismissal or appointing a supervisor with him.