what is bianca and kate realationship like in act 2 scene 1

In Act II, Scene I, Kate is basically keeping her sister captive. Bianca's hands are bound, and Kate rails around trying to get to her to admit her favorite suitor. In addition to binding her hands, Kate even slaps her sister, stopped only by the appearance and interference of their father. At this point, I'd say their relationship isn't looking very good.