Whilst I can play table tennis, cycle fast for a while, can often do short workouts, carry heavy things for a short time - walking is always challenge... Last summer I was even trying to apply for additional disability for that, suggested by my GP (glad they turned that part down tho), an alternative practitioner suggested my veins, turned out I got quite a bit of CV stuff, but no, nothing could explain it. I still definitely often have to watch out getting off my bike, esp. when next to a road - because of wobbly legs. But since taking GABA which has taken most of my stiffness, I seldom have problems going up stairs and my legs are better when walking. Now it's still my right knee and my elbows that hurt a lot, twisting legs & arms a little while walking helps. When my legs are weak I lie down before or on a bench and put my feet up. If I'm not up to it but my wife needs to let off steam, I take my bike. What's cycling like for you?
I'm pretty sure exercise would help you, as you imply yourself. I'd suggest not just 5-10' of yoga or tai chi/qigong per day, but a small workout, like the "7' scientific workout" (youtube). If it's hard for you to get going, you could start with a minute the first day, 2 minutes the second etc., or just do bits of the workout, or think up a healthy reward for doing more.... For legs chair steps, squats, plank, high knees & lunges wd be the best, and keeping it short first, maybe 10'' or 20'' with a break as long as you need.
If this doesn't work at all for bodily reasons, then that would be something to go to a doc with. I doubt a doc would do anything if you told them this, they'd tell you to do exercises too or not know what to say. That's my experience, come to think of it - however I have very strong legs, that's not the problem. Same with arms by the way: I'd've been able to do 30 pushups in 30'' on many days, but as soon as I tried to do something overhead or with stamina for longer than 3' it started getting difficult. All a bit better now from the amino acids.