This!
How long has this been going on? My ex used to wake up at 5am to train and be away from home til noon, I didn't love it, but it was his life and made him happy.
It's ridiculos that you're forced to stay in bed doing nothing for hours and hours. Are you at least allowed downstairs?
If you MUST stay at home, I'd take up reading. 2-3h of a good book with a coffee (if you're allowed one!) on a Saturday morning is rather lovely.
Really though, ignore her wishes, go get your hiking gear and climb a hill, feel happy and alive. Get back for 10-11. If she's annoyed, tell her how you feel, that being forced to stay inside the house makes you feel trapped, physically unwell etc. Have an actual conversation about her controlling tendencies, and how everyone having to follow her schedule is crazy.
Talking about time together, were tere things you both used to enjoy when you first met? What did you used to do?
Maybe organise something with her, such as an amazing meal out, a cinema visit (if she loves tv), going to the theatre, a city trip?
I used to be with someone that loved watching tv all the time. It didn't last long.
With highly stressful jobs, you both need to take care of your mental health and unwind, have something fulfilling in your life. I'm not sure what kind of doctor you are, but surely you know that a sedentary lifestyle with hours of screentime does absolutely nothing for your wellbeing.