Of course it's relevant. To forgive doesn't mean to forget. If Luke forgot who he was dealing with, that would be incredibly dumb on his part. He knew he was risking his life to save his father, which is part of what made him such a hero. When the mass murderer threatens his sister, yeah, he's going to lose control because he knows what this man is capable of despite whatever he may have forgiven.
This aspect of Luke knowingly risking his life to save his father really had a huge impact on me growing up, and I was not aware of how big of an impact it was until seeing TLJ's complete lack of awareness of this being a major part of what made Luke a hero. I have to give TLJ credit in that it made me appreciate ROTJ more as an excellent conclusion to Luke's story.
But that's just it. Vader doesn't threaten to kill her. He simply suggests that she may turn to the Dark Side. "If you will not turn to the Dark Side, then perhaps she will." "NEVER!!!" Its not like he has vision of everything he loves being destroyed. Like he has with Ben.
I don't think a lot of people get this. But Luke's willingness to run off and "help" his friends. Isn't presented as a virtue as much as a vice. It seems counterintuitive. But every time Luke tries to "help" his friends, it brings him closer to the Dark Side. Look at ESB, he goes to "help" his friends, but he gets distracted by his anger towards Vader. In the end his friends are the ones that help him. In ROTJ he's using the Force to choke, yikes! He tries split the Emperor in half. And he nearly kills his father. In TLJ he draws his lightsaber on his sleeping nephew.
This theme of saving your loved ones no matter what it costs your soul, is the focus of the PT. Look at what Anakin tells Palpatine. "I will do whatever ever you ask.......Just help me save Padmé's life." Anakin ignores what Yoda tells him. "The fear of loss is a path to the Dark Side." "I wont let these visions come true, Master Yoda."......"Attachment leads to jealousy. The shadow of greed that is." "What must I do Master Yoda?" "Train yourself to let go....of everything you fear to lose."
Which brings to the real meat and potatoes of Anakin and Luke. As you probably already know. Star Wars was heavily influenced by the works of Joseph Campbell. He says something that pertains to Anakin and Luke. This is an excerpt from the 'Power of Myth' with Bill Moyers.
"I will participate in the game. It’s a wonderful, wonderful opera, except that it hurts. And that wonderful Irish saying, you know, “Is this a private fight, or can anybody get into it?” This is the way life is, and the hero is the one who can participate in it decently, in the way of nature, not in the way of personal rancor, revenge or anything of the kind." - Joseph Campbell
You see here is the problem with Luke and Anakin. They act out of personal rancor and revenge. Their wants drive them. It's a very fine line that must be walked. The helping of their loved ones isn't done out a simple compassionate love for life, but ultimately out selfish possessive love(lust). This is very clear with Anakin. Less so with Luke, but that fact that Luke acts on his anger and hate shows that this is the case. But look at what Joseph says makes the hero.
"...
and the hero is the one who can participate in it decently, in the way of nature(I think we could easily replace nature with the Force here)
..." This is what the whole climax of TLJ is about. Luke goes from two extremes. First it's "helping" you friends no matter what, by diving into the thick of it no matter how dirty your hands get. To "helping" your friends by staying out of it completely, because he feels he's causing more harm then good. But in the end he finds the balance between the two. He finds a way to participate decently. He's learned how to be there, while not actually being there. He's learned how to fight Ben, without actually fighting Ben. He's unable to harm Ben, and Ben is unable to harm Luke. Luke is the true hero as he has learned how to participate decently in the way of the Force.