OK, hear me out.

On the basis that someone who has never seen a black hole can call themselves a cosmologist then I think I'm more than qualified to give relationship advice.
This has been going on four months, you're all climbing the walls, you need a time out to de-stress, get some sleep and get some perspective.
Probably you should both go away for a long weekend, get a cat-sitter or relative to look after the cat in your home.
Failing that one of you take a break, you'll both get some perspective.
At this point I think it is necessary to consult with someone competent who can read the dynamic of your partner and the cat and formulate a plan.
This person is more a person psychologist than a cat psychologist - holistic therapy is the big thing now.
Most cats can be made bearable, good cats even, with the right treatment and training, it does take time.
Generally they don't want to be nagging and dependent, its a lot of effort and is not good for them.
People are the bigger problem, why is your partner giving the cat a free pass on everything, not putting in the effort to develop the cat?
Lazy? Arrogant? Some psychological hangup or buried traumatic issue? Just spoiling the cat, living out something missed or missing through the cat or some other vicarious kick?
There are lots of rabbit-holes there.
Kitty daycare, catventure playgrounds, I have no idea about this at all. The age of the cat is a factor at this point, then again plenty of cats go into shelters at an older age and come out OK enough.
An issue with many cats is they are separated from their siblings too early - everyone wants a cute little kitten falling around but this is too young.
They need to develop their social skills with siblings and people, separate from the mother or they'll fix on the next mother and never separate.
Then again some cats just fixate on one person, usually a woman.
Good luck and remember to keep us updated.
(Also you can make many excellent cat toys with a sheet of newspaper)