OP I’m very fortunate in that his branch doesn’t really get sea drafts. Yes you are! The first 4 years I was married, dh was at sea or near London, whilst I was near Tavi, and then we bought a house in Plymouth (which is not dreaded at all).
You could weekend; we've done it for 4 years from Northwood/Shrivenham to Cornwall, and then for 2 years Brussels to Cornwall, but that ended up being at half terms and holidays only, as it was too difficult to get back for weekends. I gave up in the end and moved to Belgium. 13 years later, I am still here!
I was very lucky that dh managed to swerve any MOD jobs, as I would hate to live in London; too big, and I always come away feeling dirty somehow when I go there.
MQs in Portsmouth can be variable; and for my db (a Cdr) there was one option only given, take it or leave it on the Gosport peninsula next to Daedalus. He was told if he didn't take it, he would have to rent privately.
Not sure how many messes are in Portsmouth now, as Nelson has been sold off, but presumably there must be something. Friends who have to go to meetings in Portsmouth from NATO have to stay wherever they can find, so it could be Sultan, whilst the meeting is at Fleet HQ.
Evidently you are not a West Country person, any more than I am a Londoner, so yes, go back to London and weekend. Those with MOD jobs/Northwood jobs do that any way if they live in Plymouth or the surrounding area, so no reason why your dh can't live in the MQ and you come back at weekends.
You are very unreasonable in resenting the RN and what the job involves. Duties etc are part of the job and are not 'assorted nonsense'. Perhaps you need to get your head around how the RN works. It is not a city firm, but an Armed Force with its own codes and way of working. If that way of working is not followed, then people can die, either in peace time or combat. It is not and never has been a 9-5. It is working until the job is done whenever that may be. It means being sent to sea unexpectedly on Christmas Eve for an unspecified period; it means missing the birth of your child. If you resent it that much, then get your dh to resign. Just like you, I married a Naval Officer, but I was a Naval Officers daughter, so I knew that there could be pitfalls. It can be tough, but there are compensations, and I did it for 28 years until dh retired. He had already been in the RN for six years before we got together.
As to the other wives not liking you, well, do you moan about Plymouth and missing London all the time and the demands of the RN? If so, there's your answer. Have you tried phoning them, as opposed to FB invites?
Is there something you would like to do that this time away from working gives you an opportunity to pursue? You could learn to fly gliders at Dartmoor Gliding Society; you could learn to sail if that's your thing - lots of social activities there, especially if you get involved with RN sailing; you could volunteer at Saltram if the National Trust is your kind of thing.
I think you need to either move back to London, or stop missing it and make a determined effort to get the most out of where you are. Having been in Brussels for 13 years, I've had to learn to do the latter. Yes, I'd prefer to be back in Cornwall, but that isn't going to happen until dh retires again from his post RN job, so you have to make the best of where you are. It could be worse, it could be Portsmouth (and I grew up not a million miles away from there, despite being Plymouth born) and each time dh came home from seeing the appointer and mentioned Portsmouth, I told him he was weekending as I wasn't bloody well moving back up there. Luckily, he swerved Portsmouth jobs, as well as MOD and Abbey Wood, and plotted his career to his entire satisfaction.
Good luck, and in the nicest way, get a grip. If your dh stays in, you have another 12 years of this. You have to learn to deal with it. I knew another RN wife who moaned about the same things as you, We all avoided her like the plague, as she was so unremittingly negative and she didn't do much for husband's career either!