The more he pushes her away, the more she'll cling to you!
The adults need to sort this one. You as a WFH adult need to establish boundaries with everyone about not being approachable/interrupted when you're working. A quick chat and some ground rules would help. If DD is really oblivious, a sign saying "Working" stuck to a pencil is easy to hold up while you ignore, with perhaps another that days "Private" for when you're talking to your GP! 😲
If you've been a bit soft and accepted her intrusions while telling her not to, that's mixed messages and that needs to stop as it's not fair on anyone.
As for TV and your DP's unpleasant habit of banishing his DSD, why not establish a choice of one favourite show per week with each family member and they always get to watch that one uninterrupted with the rest of the family joining in or not as they please? Then negotiate the rest of the viewing. A TV in a teenager's room is not a reason to banish them nor is it a substitute for family life.
That strategy needs discussion and agreement with your DP before it's shared with the DC. If he really doesn't want family life, he's living in the wrong place, isn't he? He knew you had small children when you got together and small children have a habit of turning into big teens! They are not tiny any more and can't be out to bed after their tea; they get to have a say and a stake in family life.
The small house might be a blessing if it pushes you to solve this. In a bigger house, you might already have lost touch with everyone!
My tip, as a working parent who had one particularly demanding teen (used to come out and start complaining/unloading on me while I was still in the car!) is to build in some sacrosanct "after work transition" where you chill in a consistent spot and cannot be spoken to for 20 minutes by anyone. They are allowed to bring you a cuppa if they want to sit quietly by. Put an eye mask on if need be. Your DD may need visual prompts!
We actually built on a conservatory for the purpose and chilled there together away from all the DC (three teens at the time) with a pot of tea. It was chilly in wintertime, too, but it made all the difference. Radical solution, I know. It can work without the dedicated space, of course - you just need to decide it and be totally consistent. It's for your mental health.