Our school you can request a certain teacher (though it is not guaranteed) but I think it would be a bit unwise to ask to not have a certain teacher. Last year I listed all the teachers I was OK with. Next year I will be in a similar situation to you with my youngest and I will go to extreme measures if the normal channels don't work.
But in your case I would try just asking if your child could have someone different because they felt like they were always being compared to their sisters or because your previous experience tells you it wouldn't be a good fit.
