Is it permissible to go to a female teacher who touches students as a form of admonition, without lust, knowing that other alternatives involve immodest women, while this teacher is committed [to Islamic principles]?

Touching a non-mahram woman is forbidden, whether with or without desire. It is not permissible for a male student to allow a female teacher to touch him; rather, he must prevent her and discreetly advise her. The student should seek out male teachers to avoid temptation. If he can only find female teachers, then he should look for one who adheres to Islamic manners, and whose lessons are free from Sharia prohibitions. If he cannot find such a teacher, and he is in need of lessons, then he should choose the option with the least harm, and lower his gaze if it accidentally falls upon something impermissible.