I am having the same problem as I only bought the expensive Hunter Douglas Soft Vertical Blinds due to being afraid my dogs would ruin the Luminettes that I really wanted. Now I am thinking of using Sheers on a rod that can easily be washed and if that doesn't work out, I I will see what others suggest. I really hate how the curved vertical blinds I bought in 2006 that block the light on the sides so light from that window does not go into my open family room. They do not insulate and are only pretty when closed. I love the Luminettes and if I did not have little dogs, that is what I would have gone with as they are very expensive to clean. My kitchen and family room would be so much brighter if I removed the expensive blinds that match the wall color so well and are really pretty but they were not the right choice.

I would look at white plantation shutters for the windows and a Vertiglide on the slider since you use it every day. I would then either add a cornice over the Vertiglide or some drapery side panels. Now if you have young children I am going to change my Vertiglide recommendation to a vertical. I know no one like verticals but if you have sticky little hands, you want to be able to clean the blind easily! When they have grown to the point where you don't have to worry about that anymore, then you can move to a Vertiglide or something else. Here are some links to a blog you may want to look at for ideas. https://dressthatwindow.com/beauty-of-shutters/ https://dressthatwindow.com/i-hate-verticals-what-else-is-there-for-sliding-glass-doors/ https://dressthatwindow.com/drapery-side-panels-complete-the-look/ Not a perfect example but just trying to give you a sample of the combination of shutters, a Vertiglide and a cornice board. You can really dress up the windows on that back wall to look great! Good Luck!

If you already have a double pane door, the problem may not be the door. Before going into expense of adding another layer of drywall to the walls and ceiling and replacing the door, I would check other things. Like bathroom exhaust fan ducting...is it insulated? HVAC ducts. Plumbing vents. Gaskets on all the exterior wall switches & receptacles as well as ceiling lights. Recessed light cans? Pull a piece of door/ window trim and check that the space between the jamb and framing is insulated.

Take down the curtain rod and remove the painters tape. Since you don't need privacy, find some art that will fit on the wall by the light switch and the wall at right angles to the right side of the door.