6 year old dog with hip luxation secondary to trauma

[JuliPotter]

Dear Laurie,
I am wondering about the best treatment options for a pup with a hip luxation secondary to trauma:
Parker is a 6-year-old MN mix breed who has a hip luxation of the right CF joint most likely due to trauma; per the surgeon, Parker was diagnosed "with malunion of the right femoral neck fracture with coxofemoral luxation most likely secondary to trauma" (February 2023).

Parker was adopted in September 2022, and this issue was discovered shortly after Parker was adopted; the owner elected not to do surgery. I have avoided performing joint mobilizations of the right hip since there is a luxation but there is significant muscle loss of the right (quads, hams, biceps femoris) and limited hip extension (I did not check pure coxofemoral hip extension on either pelvic limb) and when I saw Parker last week, first time I have seen him in over a year, he also resisted my attempts to flex the hip, though he did relax while I performed strain/counterstrain of the Iliopsoas muscle; Parker was initially quite reactive with palpation of the right and left Iliopsoas, there was asymmetry of the pelvis, with reactivity to palpation of the sacrotuberous ligament on the left, there are also changes of the forelimbs and spine....I have focused my treatment on the changes/compensation I find that may be secondary to the hip luxation, or even primary concerns, but I would like to work on decreasing muscle inhibition, improving flexibility and strengthening the right rear; since the joint is luxated, what can I do?

I have attached Parker's hip x-ray and several pictures of him. The top row of pictures is from March 2023 and the bottom row is from July 1, 2024, I didn't get very good pictures/videos this time, I plan to get more.
https://photos.app.goo.gl/TNU6cFgg2BkXSmM59

Thank you so much!
Juli