What is the ruling of Islamic law concerning teaching a nine-year-old daughter to swim in a place mixed with males and instructors, even if she is wearing modest clothing, given that this takes place in the Netherlands and swimming might become compulsory in the future?

A mature girl must observe hijab and avoid unlawful mixing. Therefore, it is not permissible for her to learn swimming in a mixed-gender pool. The same ruling applies if she has not yet reached maturity but is at an age where she is generally desired. Avoid teaching a girl to swim in a mixed-gender pool due to the corruption and dangers involved. If she is compelled to do so, then necessity dictates its own rulings.