The first question to answer is, perhaps, was he always on Tatooine or did he move there?
I like the idea of him moving there more than him always being there. His answer to Aunt Beru, when she says of Luke: "he has too much of his father in him" is: "That's what I'm afraid of." I take this forward to indicate a history with Anakin and a knowledge of what he has done and/or what he has become. I like the idea of Owen going to Tatooine to escape Imperial attention and, particularly, the attention of his brother.
Owen has a different surname to Anakin but Luke maintains the surname of Skywalker, so we can conclude that he is Anakin's half-brother and not just using the name of Lars to hide from the Empire.
So, Shmi married a widower called Cliegg Lars who had a son called Owen. Cliegg owns a farm and they go to live there.
I'd like to make Owen older than Anakin. I'd like Owen to be like his father, which would be devoted to his work, satisfied with living off the land and suspicious of getting involved with the affairs of others. In this setting, Anakin's desire to become a pilot with the Republican forces would be guaranteed to cause conflict within the family. If he then came home with Obi-Wan, who tells them that Anakin has a promising career as a Jedi Knight ahead of him, I think the rift would be as wide as it could get.
Perhaps a battle between Republican and Imperial forces on the planet would destroy the family farm and Shmi and Lars with it. This would leave Owen (and Beru) needing to go somewhere to start life all over again. A planet which is at the farthest reaches of the galaxy might look pretty good at that point, especially if neither side seems to have much presence there. I'd like to see a scene where Anakin and Obi-Wan come to what is left of the farm to find Shmi and Cliegg Lars dead. Anakin tries to get Owen & Beru to come with them but Owen wants nothing more to do with them.
That would be the last we see of them until after Luke & Leia are born and Obi-Wan comes looking for them. He tracks them down on Tatooine. Needless to say, his arrival is not greeted with much enthusiasm by Owen. Obi-Wan tells them what has become of Anakin and asks them to take the baby under their care. Maybe we could see that Owen and Beru are unable to have children of their own and accept.
Anakin does not know where Owen & Beru live, does not know that Luke & Leia exist and the twins have been split up, to make them harder to find. Obi-Wan becomes Old Ben, the strange, old hermit on the Jundland Wastes. Luke becomes the farm boy. Leia becomes the freedom-fighter. Anakin becomes the baddie. The stage is set for the OOT.