Muscle loss from surgeries

Did you do any physical therapy in your rehab ? post surgery
I would keep doing what the p.t had you doing. Or ask your p.t what you should be doing at home.
If you did not see a pt after surgery, I would request one from your doctor. You definitely don't want to damage the repairs.

Start with a physical therapist. They will be able to help you address the atrophy of the muscles, help you strengthen the connective tissue, deal with the muscle imbalances that will be present and help with the soft tissue damage and scar tissue you have. Your procedures were major surgery and it's vitally important you rehab properly before moving onto a work out program.

I've been meaning to get to this, but did not have the time until now. Having one joint replaced is a big deal--having two replaced means a long recovery--as you know :-( It's not something that can be addressed with 3 months of therapy (that's what happens when you have a profit-centered health care system).

Let's also make sure we are clear on terms---you need to "build strength", not necessarily "build muscle". Muscles that have been weakened via lack of use will "get bigger" by restoring them to full function. I mention this because "building muscle" means something completely different to most people in these forums and that is not what you need.

Start with the basics:
Lying side leg lift
Clam
Donkey kick
Single-leg hip thrust
Side-steps and monster walk with bands
Wall squats with stability ball

With all of these, do them slow and controlled--focus on alignment, form and activating the target muscles.

You can do body weight squats, but I would also focus on bulgarian split squats, single-leg romanian deadlifts, step ups and single leg sit to stands. If you have some thicker resistance bands, you can also rig up a way to do some assisted pistol squats. It's important at first to keep weights low (or just body weight) and work through a full range of motion.

For knees, heel touches from a step, lateral step ups, and step downs are also useful.

And don't forget hip rotators--these aren't the easiest to isolate and work, but it's important to do so.

For core work, try arm/leg dead bug (body weight and weighted), chops, and pallof presses (esp pallof press with a sumo stance).

Examples of most of these can be found on the web and on you tube. Unfortunately, it's not easy to find an advanced training plan online--most information is for immediately post surgery, or they want to sell you something.

Here is one review that provides a longer view of the recovery process. This is following hip arthroscopy, but it is still appropriate. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3535124
Warning: this is a technical article that is written more for therapists and other health professionals, so there is a lot of advanced language. But if you can work through it, it does provide a description of a progressive program so you can see if you have any deficits, and it also gives some advanced exercises. I don't know if it will be helpful or not.

I hope there is some useful information in all of this. Unfortunately, it's not an easy topic to discuss in a forum. Ideally, you would be able to connect with a trainer with experience with this type of rehab and they could provide hands on guidance, but that's not always easy to find. Good luck.