Is it permissible to return to the teaching profession in mixed-gender schools, with the fear of falling into the sin of looking at girls who do not adhere to the legal hijab, and is this considered a test from Allah?

What we advise you to do is to look for a job in a school whose students are males, with no females among them. If you don't find such a school, then look for a school for young children, or a mixed school where the girls adhere to the hijab and the regulations of Sharia are observed. If you only find a mixed school where the girls do not adhere to the hijab, then be patient; perhaps Allah will compensate you with something better.