What an adventure! Have you seen a physiotherapist yet? If so, what does he/she say? Having someone who can actually see you, see how you move, and who knows your body is really important. Advice through the web is less likely to be useful to you. When your doctor or physio tell you that a return to yoga is okay, that is the time to begin. But, your instinct to move the uninjured side seems valid and wise. You need to move! What about asking your health care providers about doing one-sided exercises?
There are several yoga poses that are asymmetrical, and maybe you can do those on your good side, just to keep moving and stressing your healthy parts. For examples: Half-Shoelace, with the bad hip’s leg out straight (you can add upper body twists and side bends while here); Dragon, with the good hip’s foot forward; Swan, again with the good hip’s foot forward; Bananasana, moving to the side of the bad hip. In the symmetric poses, there are several that can avoid the proscribed movements you mention – no adduction, no flexion at the hip – such as Reclining Butterfly, Sphinx and Seal poses. (You can find these poses explained in the Asanas section
Obviously, these are all Yin Yoga poses, but they will help to keep your “good” side open, and should be of benefit to your whole body health due to the mobilization of chi, prana, energy. Add in Ocean Breathing
and even some earthing
while you do your practice and your immune/repair system will be enhanced. In time, you can use the same philosophical approach as you add back more yang yoga postures.