I'm not sure Anne had much choice really - neither manipulator nor trying to just grab some of the cards.
She saw what Henry had done to her sister who was cast aside once he was done with her and struggling to regain any sense of normality. Her marriage may well have become unhappy to the point of desperate - it's hard to know from this distance but I can't imagine many blokes dealing with their wife bring another mans mistress very well.
Her dad was pushing her into Henry's company, she became lady in waiting to CoA etc. Henry was bound to notice her. She refused him full sex maybe just because she still wanted to be attractive marriage material once Henry was bored? She may have held out thinking that CoA was so powerful (family) there was no way Henry would really divorce her.
All she had to do was live with being hated by CoA for a few years and resisting Henry - then she could go on and get married to someone nice.
Once it became apparent how much Henry loved the chase and was taking her 'only if we're married' thing seriously she had even fewer choices - she could hardly laugh in his face and say oh come on, you know I don't really fancy you right?
She had to continue the charade and pretend marriage to him was all she wanted. Didn't the amount of sex they had go down the pan quite quickly? Was that really all to do with Henry being pissed at having a girl and getting bored, or did Anne lose the will to keep up the pretence?
I probably don't know enough about her and there's evidence to refute the above but if not... I do wonder