Our school allows parents to ask their child not be placed with a teacher if an older child in the same family had that teacher. We cannot, however, request a particular teacher.
If that's not your school policy, we've had good luck getting the right teacher match by sending a letter describing what my child needs in a teacher. I make certain my letter describes the teacher that I feel is the best match without actually naming the teacher.
My last letter requested a teacher able to differentiate for both strengths and weaknesses and a love and depth of knowledge in science and social studies. By reputation, that ought to describe one teacher pretty clearly, and suggest that one teacher is a particularly poor match.