I'm glad that you seem to be well established in your own life. You're not dependent on your parents. Having that emancipation is huge. You can be your own person. It sounds like you are.

Your obligation, IMHO, is to be courteous. You are under absolutely no obligation to like your mother . . . or your father. That's not even something you can control. Religious leaders tell us that's why there is no commandment that we "like each other."

There are two kinds of love. One is the warm, wonderful feeling we have towards those whom we find delight in being around. We can't control when and with whom we feel that. Another kind of love has nothing to do with feelings. It is a decision to be concerned with another person's welfare. It is a commitment to be available to lend a certain level of support. That does not require that we tolerate being in someone's presence while they mistreat us. It may require us to put up with some occasional discomfort, within reason.

I don't think Skype encounters with your mother will give either one of you much benefit. I also don't think you have to provide a steady stream of emails to someone who never responds. Your mom, also, has some say over how much interaction she wants to participate in. So you send the occasional email . . . maybe a handwritten note now and then.

My father was narcissistic and difficult to deal with. When he was flagrantly insulting toward me, I was inclined to pull back and allow there to be more distance between us. Then I would leave it up to him to reach out. He was incapable of apologizing. (Though he did 2 or 3 times, to my amazement.) But when he became regretful of the distance that had developed, he would call me and invite me to some especially good dinner that he or my mom was cooking. I would accept. That was as close as he could get to taking responsibility for a rift having opened up and doing something about it.

I don't think you would be wrong to hold off going for a visit, until you get some kind of encouragement and indication that your presence is wanted. That's what I used to do. It might never come.

Here's what I don't think helps anything. I don't think you go on a mission of "holding people accountable." I don't think you berate your dad for not sticking up for you. You don't call or visit with the goal of getting stuff off your chest. That's futile . . . I believe. You focus on what behavior is acceptable, or tolerable, to you today. Withdraw from engaging with them when they don't behave themselves within reason. That allows you some control over what you'll subject yourself to.

Good luck. It'll never be easy or richly gratifying. You'll find your fulfilling relationships elsewhere in your life. Anyway, that's my take on your situation.