The fact that two characters are the same archetype and share some tropes is anything but evidence that they're the same person. In fact, quite the contrary, when one of the coincidences is DYING. Most people tend not to have lives that repeat verbatim, but even less so when it involves dying twice 
But ok, let's discuss that. The most important bit is that when you talk to him on the rooftop, Shaun says he's never set foot outside the institute before, since he was brought as an infant. So there goes that theory right there.
Plus, most of it doesn't make sense anyway, really. For a start, James has been in a vault between 2258 and 2277 and putting up with an a-hole overseer and all to protect his kid. Which makes no sense if he was a VIP of the institute, and could keep his kid even safer and healthier that way.
His search for prewar knowledge and dangerous radiation experiments to purify water also make no sense, if he has access to pretty much all the pre-war science that the CIT survivors took underground. In fact, some of the old labs and computers are still very much accessible from the institute, or viceversa, if you follow all the ways of getting in to blow them up. Plus the Institute obviously can purify enough water to even use it as decor, and it's not just recycled. In fact, it has water coming in from some very irradiated sewers. No problem there.
James has to ally himself with the BOS for his project, and later rely pretty much on just you to clear the way, when the head of the SRB is right in Rivet City.
But more importantly, really, the personality doesn't match. James is super-passionate about helping the people of the commonwealth, while Father is a complete sociopath even when it comes to his one remaining parent. (In the same discussion on the roof, when he says he freed you just as an experiment to see how long you'd survive, he also states, and that's a direct quote, "I had no expectations that you'd survive out here". So, yes, he just wanted to see how long until his one remaining parent DIES.) And the closest he can bring himself to watching the people of the commonwealth is from the roof of the CIT.
He can lie, through his teeth. He does this almost immediately when you first meet him to try and convince his parent that the Institute is not a threat to the surface when he knows about the kidnappings and the FEV experiments and the massacres. That he never went to the surface before? Also could be a lie to try and get his parent to remain below in the safety of the Institute (you know, after they proved they were worthy of leading of course, and to not run off to find their grandson the Lone Wanderer).
Shaun was not originally in charge, he had to work hard to get where he was. The Institute needed his DNA for the Gen 3 program, but once that was online and with his parent still in cryo he would have leeway to conduct his own field research regardless of radiation or risks of death.
As for the institute's knowledge, we don't know precisely what they were capable of 10 years ago. All of the fountains and such that you mentioned could be recent renovations, a show of ingenuity to the denizens of the Institute and any new scientists coming there from the outside. Of course they had clean water before, but it's just like their issue with power: not secure enough to remain completely detached from the surface. It's possible, and it has been shown, that the Institute has not surpassed the pre-war world in all technological fields due to their need for pre-war technology to make the Institute self-sufficient power wise. A GECK would function as a similar plot device.
Perhaps Shaun getting Project Purity online was his way of proving himself worthy to become the director? Becoming director was the work of decades he said, but he never said what exactly he did to deserve it. So all that crap he went through on the surface, the risks and horrors, was not for the people of the Capital Wasteland but for a chance at the job of a lifetime. It was all just a massive experiment to see if an efficient way of getting clear water could be enacted in a limited environment. The institute would need a way to get clean water to ensure it could remain permanently isolated. The sheer abundance of water we see that the Institute has, the fountains and such, could be a direct result of the success of Project Purity. They would have had clean water before but now they would never have to worry about water, so the issue when we get there is only about power.
And he would have had to leave his son/daughter in Vault 101 at least until Project Purity was complete, then he could return (with a few Coursers for the sake of "persuasion").
He is also dying of a dangerous cancer, in a world with radaway, stimpacks and, well, the institute. The last we saw of James he was being hit with a ton of radiation and if Colonel Autumn could survive then a disguised Institute scientist would have a few tricks up his sleeve. He could have used a secret teleportation device, enough for a one-way trip back home with no time to grab his only child.
The family he started along the way? It was something to pass the time, and he could take them back to the Institute to live in harmony when this was all done. His wife was also a scientist and would fit right in (she may have even been from the Institute). Maybe when Project Purity failed Shaun/James went into exile in Vault 101 and left only because there was a chance to finish what he started. Why should he go back to the Institute and face mockery? The death of his wife would have impacted him pretty hard as well. And perhaps the seeming betrayal by the world above when the Enclave attacked pushed him over the edge to make him the mean person he is when we deal with him in Fallout 4. If this were true, it would make him the most fascinating character in the Fallout universe by far.
Edited by CyrusAmell, 08 January 2016 - 03:25 AM.