That'd be a seriously long movie if it took him 12 years to find her again. Bunch of scenes of him scanning through microfiche at the library, talking to random people at bars and grocery stores, and sifting through tax records at the courthouse.... hey man if you wanna write the story, go for it
I could have blown the doors off writing another Terminator. If you could (partially) retcon part 3 and on, and keep a linear timeline?
A woman and her young child are transient drifters, with it becoming obvious that the mother has kidnapped the boy; a man who she admits to people is the father of the child is looking for them, with the mother claiming he was abusive and dangerous.
Mother Reese Harasmi and her 7-8 year old child son Conner Harasmi (as she tells people she is forced to) are a loving unit, but there is apparent mental illness present with the mother. They are a transient pair and it becomes apparent she lost custody of her child due to her mental illness, and is avoiding the law. Moments of happiness for Conner where he is playing with other children or enjoying ice cream are interrupted with abrupt, paranoid, and borderline violent moments where the mother grabs his arm and drags him away from play areas and his interactions with other children.
Mother leaves somewhat stable situations with son for shelters, or even sleeping as homeless. It becomes apparent that the father is possibly the true hero of the story, as he may be trying to rescue his kidnapped son. Mother becomes paranoid around police, and even other government officials at shelters and food-banks.
We meet Ken Styles as he enters a Police station and asks if anybody has seen his boy or his mother who kidnapped him and lost custody due to mental illness. He breaks down to the clerk and states that this boy was his everything, and that she took him. You only see snippets of the father from behind and on weird angles, looking downtrodden and desperate to find his boy. You never get a good look at him until later in the movie.
The son begins to suspect his mother is mentally ill. He loves her, but he seems to want to get away, and says he liked staying with his dad. He wants to go back to his dads house. His mother tells him that wasn't his real dad; that his father was an important military man who traveled a lot, and that any man, or anybody else that wants to take him away from her is very bad, and may even have to die. The son, crying, tells his mom that dad never abused him, and he never saw his dad hit her, either. Emotions weigh heavy through scenes of poverty and a childhood being lost. The mother seems to become more violent, and when a couple other homeless children try to steal the son's toy gun on a train they hopped, the mother steps in and restrains the older child, and forces her son to beat the other child with the toy gun until it breaks. These are dark scenes. The tone of the movie has been dark and sad up to this halfway point.
I'm going to stop now because I didn't plan this out and started spewing it out just in response to your post.. But basically, I would have made the movie in a similar tone to the first movie, but a bit more emotional drama than horror, with horror elements emerging in the second half. I would have it revealed that this was a Terminator movie near the end. I can think of a bunch of ways to go.. The mother sees a digitally altered young looing Kyle Reese on a news program or in a national paper, and this is what leads her to go back to the city in California.. But she brings Enrique and company as back-up after a stop in the desert and they help destroy the Kyle Reese clone robot once it's discovered what he is etc.. She gets caught at the end and sent to Pescadero mental institution and you find out at the end that this was a prequel to T2, and you see John (Conner) being told that his mother was crazy, and nothing she said happened really happened. You find out the "father" he was talking about was his first foster father he was with for a few years, who has been killed, and he is sent to stay with Todd and Vasquez.
TL/DR make a dark prequel to T2 with a similar tone to the first movie, with a lower budget but still a good amount of marketing. Allow the word of mouth spread about the twist ending that was not given away in the marketing of the movie. NOTE: I never watched the Sarah Connor chronicals.
Anybody see what I did with the names? It's pretty obvious lol