I think one thing people don't take into account with Thad, especially when it comes to his post-Impulse appearances, is anger.
Specifically, how it is such a strong motivator and how it is not always rational. How he still goes after Bart in his post-Impulse comic appearances makes sense when you look at it from the perspective of anger and how Thad is such a prideful individual.
His actions can easily be chalked up to displaced anger towards Bart because 1.) He can't exactly go after President Thawne because he views him as a father/his creator (I assume standing up to him would be incredibly difficult because he views him in such a way but also Pres. Thawne's also proven himself to be manipulative and controlling) and 2.) because Bart had a part in essentially ruining his life or at least the perception of life being good. Bart played a part in shattering the truths of Thad's life. Thad thought his life was fine, that he was going to make his family proud of him, that he had a part in it, that he was family to the Thawnes, but instead he learned that he was being used, manipulated, and that he was unloved.
If you, a prideful individual had your perception of reality shattered by someone would you take a helping hand from the person who shattered your reality? I think not. So instead he goes after Bart. He's someone that Thad can actually hurt. Someone he can take his emotions out on. It's misguided and maybe not rational to the readers who understand his situation better than he does, but Thad is a misguided character.
I think his anger towards Bart is what prominently drives him post-Impulse actions and that it should be taken into account more.
