moving because of the Navy

I think it was pretty accurate. An E-7 (Chief insignia in the film) would have accumulated a lot of 'stuff' over the years (7 minimum, usually much longer, 12-15 years in the Navy), and the military only pays you to move a certain amount based on paygrade and time of service.
Anything extra you have, you either leave it behind, have a 'PCS' garage sale, or find some way to drag it along because you sure can't afford to pay the government for the 'overage'.

My father was career Air Force enlisted, and the last four times we moved it was dragging all sorts of trailers and extra cars, enlisting family members for help to drive our stuff to the new station.

Usuualy, when a movie thaqt is supposed to be based on a true story, they usually do make up things for the movie, but in characters that never was around in real life, etc. Well maybe the Navy coun't afford to pay him to move, or just didn't want to, and I don't really see anything in the trivia section about this.

While it is true that the military moves you, that can often take a fair amount of time. It is entirely plausible that the military moved most of their goods, but they packed up a trailer full of things that they needed immediately and hauled them on their own.

Military families are given the option of packing and shipping their own stuff during a move. The military will pay the service member a large percentage of what it would cost the government to pay a moving company to do the same thing. This type of move is called a DITY (Do IT Yourself) move. It saves the government some money and while allowing the service member to make some extra cash. It is certainly a bit of a hassle to rent the moving truck and pack the stuff but the average underpaid military family can certainly use the $500 - $1000 (profit) that comes from making the DITY move. I made a couple of DITY moves early in my career because we could use the extra money. I could imagine the Morris family doing the same.