Is it permissible to despise a mother who is ill-mannered and harsh, given the obligation to obey and honor her, and Allah's saying: "And if you had been rude [in speech] and harsh in heart, they would have disbanded from about you"?

What you mentioned about your mother is a mistake on her part, but it does not justify disobedience to her and abrogating her right to dutifulness. Patience with a mother's harm and harshness is obligatory. We have previously issued several fatwas regarding how to deal with a mother who mistreats her children. Merely disliking your mother for her bad behavior, without expressing it, does not entail sin.