Same old: ask your doctor first. You can pretend you're in the gym if it helps. Just pretend no one else is there yet, so you don't have to be macho with these moves. Morning and evening reasonable is better than macho.
PS. You really can do the bun squeeze (not fiercely) almost anytime. (Maybe that IS part of your brother's workout.)
I also do something a white-haired yoga teacher taught me: squeeze the tummy muscles 10 times but NOT after eating dinner.
PPS. I do other balance stuff waiting for the water to heat or whenever:
Just stepping from side to side like a new dance step the others haven't heard about.
Now the arms: I still get out of bed the hospital approved way: Starting on my left side (that's the side where I can get out of bed) using my left elbow to push up to a sitting position as my legs go over the side so I don't twist at the waist. Many mornings the left elbow is positive it can't do this, but it usually can.
Then plastic bottles of shampoo & conditioner and into the back support chair. Your physical therapist has probably told you how many ounces for each hand. I gently swing the arms from the shoulder, back and forth ten times. Rest. A few deep breaths. 10 more. Then extended arms up and down gently. Not too high at first. 10 times.
Then at shoulder height, "rowing" in and out. Ten times. Rest. Breathe. Again.
With your back supported, my secret "imitate moving your wheelchair." Ten times may be plenty.
CLIMB: No matter what the PTs taught me, I do NOT go down stairs without a railing. But, fresh out of rehab I went up some outside stairs to a restaurant I needed to visit to feel human again. There was a good railing, and someone behind me in case. I also go up the stairs in the library (good railing and my cane.) I do NOT come down stairs there. Falling up may break my glasses. Falling down may break everything.