I guess Ned's promise ran so deep that he didn't even tell Catelyn the truth. So that hate...it was entirely misplaced, but I'm sure that doesn't make it any easier for Jon to bear or you in the waking moments of remembering it. At least in Lyanna's case...she had no choice.
I think you're allowed to be mad and tired and anything else that you're feeling. What's happened to you - like what happened with Jon - isn't at all fair. It's not how families are supposed to work, especially when it was all out of your hands and you had no control over your situations. I think the important part to remember is that it's not your fault either, Max. Nothing you did ever caused any of this. Your existence is never something you should apologize for and it's not a mistake. How those women treated you, in real life or in dream, that's on them. That is their burden and shame to bear. It's their damage, baby.
And you...you have risen above it all and turned out to be this amazing, kind, upstanding man in spite of what they did. I know it hurts...I know it hurts to have the people that you want to love you - the ones that should love you - turn their backs and beat you down. It's the worst feeling in the world, but you can only control yourself and how you handle it. I've found that the life in the dreams reflects my real life a little too accurately for my comfort, too...so I understand. It's exhausting and maddening and I just have to keep telling myself to pick up and get through it.