IMO, ballet will give you more coordination, and perhaps flexibility. alot of "on your feet" work, which can help you with your lateral movement.
yoga will be overall balance of your body, flexibility and static holds for the most part. pilates will incorporate the same but with more movement, in general. I'm not sure how much movement there is on your feet though, which might be a deciding factor since you play standing up.
have you looked at martial arts? more balance, more focused on strength, flexibility and coordination. also you are dealing with balancing yourself by being offset by others. Judo or a grappling art would be a good choice.
what position do you play?