While I more often see the other way around, I tend to view Drew's family relationships as being much closer than May's.
So in Shining Justice, Drew's father is Scott. I have mentioned this before, and during the watch party earlier today I even made a joke about how my headcanon actually made sense.
The reality is that I made it up to actually have Scott be a dismissive father to Drew, but since Scott is familiar enough with contests to analyze them, this didn't really hold up.
Drew's mom's hair is green. That's all I have.
I also like to think that Wally is Drew's cousin or something if he exists in Shining Justice*. As you may know, Drew is sort of based on Wally. See, the earliest forms of what I'd call Shining Justice from around 2018 or so was effectively more a fusion between the anime and the games, and when I got the ancient ass fanfics involved to make the first of modern Shining Justice, that part didn't exactly go away. So therefore Wally exists, and I felt it made sense to make the two related. I was initially thinking brother, but I realized that didn't add up earlier this week while writing about LaRousse.
As for May's family? It's actually more dysfunctional.
I do think there was a focus on Pokémon versus other aspects of life in May's family. While it's a common belief to attribute May's dislike of Pokémon early on to the Tentacool when she had the incident with them, I personally think it's more that May learned a grim lesson either following the incident over a longer period of time: that her parents care more about Pokémon than about her. Thus she associated Pokémon with the lack of parental love she felt.
I also headcanon there is parental favoritism at play. Max is more interested in Pokémon than May is. Therefore her Pokémaniac parents probably gave Max more affection which further reinforced May not caring for Pokémon.
As for Max? Well we all know Max. However I actually have a similar age gap between me and my younger brother and thought Max was a year younger than he was in canon because when I was 10 my brother was 6. Or rather he was 7 for like two weeks and then I turned 11.
Hmm, maybe should write something about this.
Both meeting each other's parents would go rather smoothly.
With May's family, in canon Caroline definitely approves of Drew, and even teases them about romance. I see no good reason why Senri** wouldn't approve of Drew either. Senri is definitely less observant about romance than his wife, however.
In Shining Justice, she likely would meet Scott under very different circumstances. I don't want to get into it without major spoilers for ideas I might not follow through on. However, I do think Scott would think May is a pretty cool girl.
*He probably does tbh but I'm not 100% certain on it and his narrative role really overlaps heavily with May in Shining Justice.
**Norman is referred to using his Japanese name, Senri in Shining Justice.