I mention them now, I will not mention them again. It is not lack of love nor lack of sorrow. But the iron thing they carried, I will not carry.
Our speaker seems to want to make it clear that she is moving on not because she doesn't care about her parents or respect them. It's just that she doesn't want to live with the same weight of unhappiness. She wants to love her life.
Hey, fair enough, speaker. You go on with your bad self.
I give them—one, two, three, four—the kiss of courtesy, of sweet thanks, of anger, of good luck in the deep earth.
Our speaker symbolically kisses her dead parents good-bye, expressing her respect, thanks, and anger, and wishing them luck.
These lines capture the emotional conflict we often feel toward family. Obviously the speaker is grateful to her parents for the fact that she, you know, exists in the first place. And she's probably thankful for their love (however flawed), and everything they provided.
Basically, she wants to be courteous, but also to acknowledge her anger. They weren't perfect. Her father especially seems to have done a number of hurtful things. Still, that doesn't mean she doesn't wish them well in the afterlife, "in the deep earth."
May they sleep well. May they soften. But I will not give them the kiss of complicity. I will not give them the responsibility for my life.
Our speaker wishes her parents the best, but she won't put the responsibility for her life on them or what they did.
"May they soften" seems to recall that image of iron our speaker used earlier. She hopes that in death her parents can lose that hardness and bitterness they carried in life.
Of course, "may they soften" also kind of reminds us of a corpse decomposing. Gross, but on point.
That last line drives home the speaker's philosophy: that she alone is responsible for her own life and happiness. She refuses to mope or to blame her parents for the way she is.