Joining in on the Sims 2 headcanon/interpretation thing (because I love fictional drama and adding a little chaos to the households), and I’d go so far as to say that both Buzz and Lyla are/were bad parents.
In my opinion, Buzz isn’t just a villain and Lyla just his victim (come on, let’s be realistic, the only victims here are Tank, Ripp and Buck), and in fact, I see them both as complex flawed people who played a role in the dysfunctional family dynamics of the Grunt household at the point where the story/game begins.
Buzz may be a jerk who (currently) only cares about fighting whoever he dislikes, hating aliens, and turning Tank into a younger version of himself, but let’s not forget that Lyla (after divorcing Buzz) left in the middle of the night, leaving her children there with their controlling father (and the fact that she taught them basic things like talking, walking, or using the bathroom doesn’t mean she was the most loving mother or that she cared much about her children; that’s simply the bare minimum you would expect from a parent).
Since we have nothing else to base her character on (and sadly we don’t even know if she had a job or who she knew or was friends with), based on Lyla’s personality traits, aspiration, and interests, I picture her as someone who simply followed her wants, whims, and impulses of the moment. I headcanon her as a messy/disorganized free spirit who didn’t give much thought to the long term stuff, clashing with Buzz’s completely opposite personality who, on the other hand, is someone obsessively calculating, perfectionist, and strict.
While Lyla is nice and playful, Buzz is grouchy and serious. While Lyla has the lowest points on these interest categories, Buzz's main interests are Politics, Crime and Sci-Fi. While Lyla is a Romance Sim (these Sims are known for their lack of lifelong commitment in relationships, not caring much about what others would think of them as long as their desires are fulfilled), Buzz’s aspiration is Popularity (not only wanting to have successful parties, but also wanting to befriend many Sims and, over time, become best friends, reflecting a desire to maintain long-term relationships and be liked by others).
I imagine their relationship started out as something that both of them selfishly saw as beneficial for themselves at the time. Lyla was probably a popular girl whom everyone liked because of her fun and pleasant personality, so my theory is that Buzz wanted her as his girlfriend because she helped boost his image of the popular, winner guy (I also think he would have used her to maintain his macho image, but that’s a rant for another day). Lyla, on the other hand, probably saw Buzz as the typical successful and athletic guy to hook up with and then move on to the next, perhaps not having much interest in him beyond his looks (and considering that her highest interests points is on Money and Paranormal, maybe also in a financial sense). I think their relationship developed too quickly and both of them (though especially Buzz) were expecting things that were impossible and incompatible with the other person’s personality because they never truly knew each other until it was too late and kids were involved.
The relationship between these two was doomed from the start because they were both selfish and unfair to the other and the ones who paid the highest price were Tank, Ripp and Buck.