Is money earned from dual employment in teaching, with the knowledge and cooperation of both parties, considered unlawful wealth due to violating statutory law that prohibits dual employment? And what is the solution if that is the case?

The money you received from both jobs is permissible (halal) for several reasons: you fulfilled the requirements of each job with permissible benefits, each party was aware of your work with the other, and what the university provides is considered a scholarship to complete your studies, not a duplication of employment.