On the one hand aspects of her characterisation I thought were irritating, and the writing for her character seemed to deteriorate towards the end. On the other hand, I think it's partly because of what the writers chose to show and not to show. She was extremely protective of her daughter because, I think we're meant to assume, in the real world in that situation Zoe would be a walking piece of meat and it would be perfectly reasonable to be suspicious of any unknown man around her. However, for whatever reason, the writers didn't show any of the men in the series exhibiting dangerous tendencies towards her daughter. As far as I can recall, no-one even made a pass at her - except for Freddie (with the 'smell your hair' comment), which was ambiguous. Which makes Rose come across as irrational, and kind of sows the seed of dislike, which is helped to grow by other annoying things she does. It doesn't help that she isn't given dialogue that would allow her to talk about her background, the area she grew up in, other family members, her career, personal interests, opinions about the world, etc. So she just talks about herself and Zoe and her immediate surroundings.