Yeah if anything I would say Ned had his own sense of honor. A sort of self righteousness if you will. Taking his nephew and letting his wife think he cheated on her caused more issues than I'm sure it was worth. But he was keeping his promise to his sister, which he placed in higher importance than the trust of his wife.
Even hating Jamie for killing Aerys Targaryan. He knew Jamie did the right thing. But he hated him for it.
Letting Jon Snow suffer and never know the truth about his mother... that wasn't right and it was the reason for a lot of unnecessary conflict.
Even let Jon go to the wall, without the knowledge of his true lineage. Maybe if Jon knew, it would have changed the trajectory of his life and made him feel as if he had a place in the world.
Still missing the point.
Ned and Catelyn had the healthiest marriage of any of the big couples in the books. They raised smart, disciplined and just being honest impressive kids.
Jon Snow was definitely a sore point, but it was a small price to pay to ensure his sister's son had a happy childhood home, which he did have.
It wasn't until he got the Wall that he understood this, but it's the truth.
Jaime did not do the right thing.
Once he killed the pyromancers, the immediate threat was gone. Subdue Aerys, turn him over to the rebels and maybe ensure his princes kids don't get murdered and the wife raped n then murdered as well.
Jaime killed Aerys for his own satisfaction, and then did nothing while the remaining royals were brutalized by his father's men.
A trial for Aerys would've tied the rebellion off neatly, but instead his sworn guard cut him open from behind, sullying the movement.
He should've told Jon, true but again, he was thinking about the safety of the majority. Jon is safe in a Stark institution, and not getting himself killed seeking out his crazy relatives across the sea in exile.
If you think Ned was self-righteous, you're not paying attention.