I think the difference in how Rhaenyra reacts and how Aegon reacts to losing a son, is honestly just a dynamic of the general difference in emotions between men and women, in my experience male sadness is often manifested in anger immediately where as women are more prone to sadness and crying as we saw with Rhaenyra and then once this passes she wants blood. The characters are obviously very different but I think they both really loved their children.
This is honestly how I saw it as well. I don’t mean to generalize of course, these things can vary, but Helaena’s grief manifested similarly to Rhaenyra’s as well. Most men tend to grieve through rage. I am also certain that they all loved their children.
You are correct about people saying bad things about yourself and there is nothing you can do to convince them otherwise. I found if someone is bound and determined to see you through sh*t stained glasses, and misunderstand you at every turn, best thing to do is walk away, and avoid that person. Ignore them. You could even save that person's dog from a burning fire, and that toxic individual would say how you would do anything to get attention.