I usually play challenges, so my gameplay tends to be more strategy than story. In my randomacy, one of the goals I rolled was perfect children. It hasn't been updated to include Parenthood yet, but considering the goal was about striving for perfect kids, I played it so my sim's offspring for that generation couldn't receive any negative character traits and tried to have each of them earn at least two positive ones. The relationships between the kids and their parents were all daddy/mommy dearest by the time they reached YA, which, if I remember correctly, is described as having the best relationship with little discipline.
On the other hand, my rotational save has some storyline going on for different families. One of my favorites at the moment is the Fengs. MCCC gave Victor and Lily a son, and while they were together, I played it so their son was mainly cared for by his nanny, whom Victor was having an affair with and eventually left his wife for. They moved into the apartment across the hall and have since started their own family, leaving the son with his mother. Lily has the hates children trait, so I've been playing her as cold and distant and even resentful of her son, which spiked when Victor left them. I see her ignoring his victories and biting at the heels of his shortcomings, whereas with Victor, I see him ignoring him, period. He's moved on to his other family.
Once the son reaches YA, I want him to be responsible and have good manners, but insensitive and possibly argumentative due to his upbringing by Lily. I can see him having trust issues because of what happened between his parents, so I think the jealousy trait would suit his character perfectly. I want him to be resentful of both his parents as they're both pretty awful imo, and likely cold towards his half-siblings for having it easier than he did. It's going to be a mess of a family; I'm looking forward to it.
Oh, and it might get even messier. The nanny wasn't the only woman Victor was seeing behind his ex-wife's back. He's also seeing Nancy Landgraab, a renowned criminal, and an alien with a vampire roommate who was quick to take care of a vampire who broke into their house to drink from her. Also, his new wife has the jealousy trait and wants to be a master vampire—just imagine what she could do to him if she found out he was cheating. And to top it off, he caught fire while cooking in his new apartment the day he left Lily. Karma is coming for him.
I'm loving it.