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Brock and Misty have known each other since they were both teenagers, having traveled with Ash and later both being Gym Leaders in neighboring towns. They were good friends who saw each other frequently and over time romantic feelings began to develop. They were married in 3614, 9 years after they first went on their journey with Ash. Their first son, Petrus, was born two years later, and their second son, Seneca, was born four years after his older brother. However, by this point, Misty and Brock’s relationship had started to become strained. They both were very busy with their Gym Leader jobs and felt like they never had enough time to spend together or with their sons. They did try to set up regular dates where they’d leave their gyms and kids with one of Misty’s sisters or with Brock’s brother, but even then they just didn’t click with each other anymore and they’d often end up arguing and not having fun. In a last attempt to save the relationship, they decided to have another child, hoping that would help bring them together, and Alton was born two years after Seneca. Unfortunately, nothing changed aside from there being another baby in the house, so Misty and Brock decided to divorce, since they clearly weren’t getting along as spouses and trying to force the relationship was just making them and their children miserable. The divorce was finalized when Alton was about one and a half, and Misty and Brock decided to share custody.
Both of them wanted to try and take some time to find themselves after ending the relationship, so for about a year after the divorce, their sons ended up staying with their Aunt Daisy and her family in Cerulean. Brock officially handed his Gym over to Forrest, then traveled to Sinnoh to study pokémon medicine, which is how he met Autumn and ended up eventually dating her. He kept in regular contact with his sons while he was abroad, sending souvenirs and video chatting regularly. Misty decided to go back to the Orange Islands, leaving the Cerulean Gym with Daisy, which is where she reunited with Rudy again after so many years. The two hadn’t ever known each other that well when they met as teens, but they found they got along quite well as adults and Misty also grew fond of Rudy’s daughter, Adriana. Something can probably be said for how badly Misty and Brock’s marriage had deteriorated that they both ended up finding new romantic partner’s fairly soon after divorcing.
Brock moved back to Kanto and bought a small farm near Route 3 where he opened up a pokémon clinic for both his neighbors and any passing by trainers. Autumn moved in with him not long after she finished up her studies in Sinnoh, bringing along her Miltank and adding a dairy business to the farm. The two had a daughter, Harvest, together about a year later. Misty decides to officially leave the Cerulean Gym to Daisy full time and move in with Rudy on South Mandarin Island permanently, also getting a job for a local aquatic conservation group, working with water-type pokémon, as well as helping out with her husband’s gym. After they settle down, their sons end up splitting their time between them, spending their weeks with Brock and Autumn and going to school in Pewter, and spending their weekends and most school breaks with Misty and Rudy in Trovitopolis.
Petrus and Seneca both grew up fine with this arrangement. They got along well with their sisters and enjoyed growing up in two different places. Petrus ends up befriending Kestrel, Janine’s eldest daughter, and eventually falls in love with her, so after he moves out he mainly spends his time in Fuschia trying to woo her. Seneca greatly enjoyed helping out on his father’s farm growing up, so he spends most of his time there, where he’s also studying pokémon medicine from Brock and how to take care of farm pokémon from Autumn. Alton, on the other hand, hates his family situation. Perhaps it’s because he was too young to remember anything else. He doesn’t like how he has to always travel between his mother and father’s house, how he has both a stepfather and a stepmother as well as his birth parents. He doesn’t like how Brock left his family to go off to Sinnoh, enough that Alton changes his surname to Misty’s once he’s old enough. He doesn’t like his mom much either, but he respects her for her work so she’s higher up than Brock. Misty is probably the family member he gets along best with, aside from his siblings, since they have a lot of interests in common. Alton wants to work with oceanic conservation just like her one day. Alton in general is just prone to holding grudges and he just wishes he could have had a ‘normal family’ so his annoyance at his family situation grew into resentment over time. He ends up spending a lot of time with the Oaks in Pallet rather than with his own parents, since Sage is his best friend and ‘the only one who gets him.’ He also eventually runs away to Almia to become a pokémon ranger without even telling his parents. Alton is still a teenager, however, so as he grows older, I think he’ll be able to put some of his grudge behind him and try and bond with his family more.