This is long, sorry - but I'm in a real quandary over this!
We got a cat about a year ago. Partner grew up with cats and wanted one. I am the polar opposite of a pet person but thought it would do him good as he is not great at expressing his emotions and thought having a pet would give him an outlet for affection etc.
We wanted to get a rescue cat, maybe a bit older, but no shelter would home with us because we had a toddler (she's about 2.5 yrs now, very very gentle but they didn't care). We heard of a lady fostering a rescued kitten via a Facebook page, she checked us out and was happy with us, he came to live with us at about 12 weeks old.
Problems started almost at once - he was very aggressive, kept biting and clawing and attacking our feet every time we came into a room. However we figured that was just kitten behaviour and he'd grow out of it if gently discouraged. It didn't he got worse. When he was old enough we got him neutered and he settled down a bit but not much. We felt persecuted every time I came into a room he was in as I couldn't relax, he was always trying to bite us or scratch us and would never leave us alone. But we persevered as we'd made a commitment, hoped things would improve.
Eventually when he was big enough we fitted a cat flap, and he became much better - spent a lot of time out of the house, and when he did come in was much more relaxed. We make sure he had all vaxes, use Spot-On religiously every 30 days. Thought things were on the mend.
But since summer he has begun shedding hair constantly - literally can't stroke him without huge hanks of hair coming away.
I don't think he's ill - full of beans, very glossy, no thinning of the hair - it just keeps coming! It covers every surface, gets on all our clothes, is clogging the washing machine. It drive my partner (who is very fastidious around the house) INSANE. Doesn't bother me so much, but my partner won't stop moaning and it is ruining our home life as he won't ever just settle down and relax, always chasing the cat around with the brush or chasing me/DD around with the sticky roller. Cat is white so shows up on everything. Means DP is very critical of cat and not very nice to him (not abusive, just won't let him sit on his lap as fur, tries to brush him all the time, doesn't have a kind word for him as so frustrated). I didn't even want a cat so find it hard to be affectionate to him, I had expected DP to do that as he wanted one so much!
Additionally, despite the Spot-On, he has started bringing in fleas. DP and I both regularly bitten, though DD seems immune. Have flea-treated the whole house to no avail (he's only allowed in the kitchen and one other room downstairs now anyway after clawing up the carpets upstairs). Fur I don't mind, but parasites make my flesh crawl.
And he still claws and bites (playfully, but even so) whenever we try to stroke him when he comes to sit on our laps. It's more like having a dog than a cat, he can't amuse himself when we're around, just wants to chase our hands and feet all the time!
Fundamentally, we don't enjoy him, and we shouldn't have got him in the first place. But we did, so I'm trying to work out what the best thing to do is as I can't take another decade of the constant bad atmosphere in the house his fur and general behaviour makes with my DP. Nor can I abide the fleas.
So should I:
a) try to rehome him with someone who will love his playful, needy personality (feels irresponsible but has potential to be a good outcome for all of us)
b) turn him into an indoors only cat to deal with the fleas (still leaves the fur problem, and seems cruel as he loves outdoors)
c) restrict him to the kitchen and the outside world via the catflap (controls the fleas and the fur, but doesn't seem much of a life for him as won't get much time with us)
d) Suck it up as it's our own fault for getting him, and be miserable for the next 10-15 years
e) Rehome DP so I don't have to listen to him complaining? 
If anyone has any top tips re fleas and/or fur then I'll try anything, but we already brush him all the time and use the Spot On so don't know what else we can do!! If we could get even the fur under control the rest would be bearable I think.
DD doesn't care either way, totally ignores him most of the time.