There are various ways to strip enamel paint (which is probably what you're talking about) from styrene. My own old favorite is automotive brake fluid, which I've been using for the purpose for about thirty years. Other modelers say they've had better luck with oven cleaner.
I don't recommend laquer thinner. It's a solvent for most types of styrene.
I imagine the kit in question is the one originally produced by the Ideal Toy Company (ITC) in the early fifties - when the ship herself was the very latest in high-tech ocean liner design. Revell also produced a model of her at about the same time, but the Revell kit was considerably smaller (1/602, according to Dr. Graham's book Remembering Revell Model Kits). There may have been others, but if so I haven't heard of them.
The ITC kit was reissued by a company called Glencoe fairly recently; if your father bought your kit ten years ago, it's probably the Glencoe version. It's taken quite a bit of criticism in the modeling press. A couple of points need to be born in mind when looking at such kits. One - the early fifties were in many ways a "golden age" of plastic kits, but the standards of precision and accuracy we take for granted today hadn't been established yet. Two - The United States was built under a big federal government subsidy, with the provision that she would be available to the Navy in wartime for use as a high-speed troop transport. Many of her high-tech, state-of-the-art features were classified for many years. I suspect, in fact, that the model companies weren't able to get access to any genuine, authentic plans of her, and based their kits almost entirely on photographs. (Her underwater hull lines remained classified for many years. I've often wondered whether that's the explanation for the odd design of the Revell kit - with the hull sliced off just below the waterline.
I had the opportunity to go on board the United States one afternoon back in the early eighties. At that time she was berthed at Norfolk, Virginia, and her then-current owners were talking about converting her to a Caribbean cruise ship; the museum where I was working was hoping to acquire some interesting artifacts before the conversion started. We did get some good stuff out of her, but of course the conversion plans didn't fructify. I saw her briefly from I-95 when my wife and I were passing through Philadelphia a couple of summers ago. She's a terribly sad sight. I do hope her story has a happy ending, but it's tough to be optimistic.
Anyway, best of luck with your project. I agree: for the sake of both your dad and the memory of the ship, it would be best to represent her in her glory days.
Youth, talent, hard work, and enthusiasm are no match for old age and treachery.