What kind of relationship did Anne Boleyn have with her mother?
It is impossible to know. All we can do is hypothesise and I think Anne Boleyn's words in the Tower, when she voiced concern over her mother's welfare, speak of a love and closeness. Anne wept and said:-
"Oh, my mother, thou wilt die for sorrow with much compassion" and Alison Weir points out (on p141 of the hardback version of The Lady in the Tower) that one of Lady Lisle's correpondents had written of how Elizabeth Boleyn was "sore diseased with the cough, which grieves her sore." Anne was obviously worried that news of her arrest would make her mother's condition worse.