They've spoken at length with DH (now they're older), how difficult they found it that they liked me, and had fun spending time with us, but because they knew that mum didn't like me, or me being in their life, they felt they shouldn't either.
Yup - my DSD has also said this to me and DP; in her case, she refused to have anything to do with her Dad or me for over two years, because he refused to choose between me and her when she gave him an ultimatum.
Her Mums open dislike of me caused her a great deal of emotional conflict - she knew (in her mind, whether it was true or not) that she would upset her Mum by spending time with me (because she knew that her Mum didn't like me), and yet, she wanted to spend time with her Dad, so her "solution" was to tell Dad to get rid of me!
With younger children, it also has an impact on their feelings of security - they have to try and work out why their Mum repeatedly places them in the presence & care of someone that they say that they don't like. In my DSS case, that has led to a situation where he feels insecure when he is in my sole care, and isn't comfortable when I drive, rather than DP, for instance.
Negative language, alienation, badmouthing and discouragement can all be prevented by Court Order in some States in the USA; because the courts have accepted the research and evidence that reveals just how emotionally harmful it can be. There is now a great deal of work being done in the UK as well - hopefully, this type of behaviour will begin to be acknowledged by CAFCASS and in Court to avoid DC's being put through it.