She's a great actress doing a fantastic job of playing a very unlikable character. Except that she's not unlikable in the way a good unlikable character is. She's not the way OP is feeling about Q.
But it's not just the way she interacts with Data, which does result in character growth for both of them. I'm sure they were going for the adversarial thing but it didn't work, with Data or anyone else.
He's like Murdoc from MacGyver. You hate the character but you can sense that he's going to be defeated eventually and it'll be a fun ride getting there.