Its fine to find it hard but unless your planning on moving out you need to find a way to deal with it.
they’re always in, so there’s never any privacy or quiet
Go for walk, go to a cafe, go to the gym, Get some Noise cancelling headphones and listen to music, spend weekends at your own parents.
They’re always watching tv so we never get to choose what to watch
Watch things on your phone/tablet/laptop. Buy/borrow a tv for your bedroom.
They cook dinner every night which are actually really nice but I miss cooking myself. I offered to but they said it’d be a waste of electric cooking a whole other meal.
This sounds like you offered to cook your own meals, not that you offered to cook for them. Tell them you would like to cook them a meal at least once a week.
I don’t have a key so I feel like a guest
Offer to pay for getting new set made.
they have a dog who barks when we come in. Because parents go to sleep early we can’t get in past 10pm because they’ll be annoyed at us for waking them up.
Let them know ahead of time when you will be in after 10pm, stay with friends or go to your own parents at weekends so you can be out later.
they’re always asking questions like what we’re doing, where we’re going, if we’re back for dinner
Surely this is just normaal life living with other people. Don't you ask your partner where he is going and when he might be back when he leaves the house?
Be careful your not projecting your frustration with your situation onto your partners parents. And I would seriously consider spending a few weekends a month at your own parents. 2 hours is not that far away, my parents used to live 3 hours away and I would go home almost every weekend.