Indeed airline!

I've done Houston multiple times before on a TA-USA connection and there is no way she can do this without at least a "safety blanket".

Need convincing? Explain risk of furthest away gate at arrival and furthest away, always on the other side, gate for her connecting departing flight. It can add up to multiple kilometers worst case scenario, esp. if she is better off uing elevators instead of stairs. Can you do that here at home mom? (use an example in her home life that has a likewise distance) Now add in standing at customs for x-time, explaining that if she is lucky it can be very speady but since she is recovering she will be a slower walker and thus have at least one flight very likely almost 90% in front of her, so that adds to her waittime now. Can she do both? Now dear mom, love you, but add on the fatigue you can get run into after a long flight. Combined with having been in a seat that might have been a bit harsher on her healing body than it would've been normally. Is she still 100% sure she can do that all?

And no need to worry about "looks" or judgements, since she will never see those folks ever again, being just in transit.

Is she still a tough cookie to crack? Mom, what if heaven forbid something were to happen that runs up waittimes at CPB and/or TSA like extra safety measures because of a higher risk, another incident like a recent bombing or whatever? Waits can add up big time, can she still stand comfortably and safely (latter is a big thing with some elderly, stubborn about pain, but more sensitive to risk of overdoing it to the point of becoming a risk of falling or alike)