In the story, she "felt bad for her family" as she used to go home late due to selfish drivers not yielding, blocking other cars. Can "bad" have the meaning of "sorry"? The translation is "feel sorry for", but I guess it means "feel upset or something".
3-3)So not only wereher fellow drivers angry at her, it was actually taking hereven longer to get home after work. Kate’s children were almost ready for bed by the time she walked in the door. Feeling bad for her family, Kate gave up on her plan of not blocking the intersections and went back todrivinglike everyone else. But unknown to Kate, her neighbor Joanne, had come up with the same idea a couple of weeks earlier.
"Feeling sorry for" is right.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.