I've been in the same situation - basically, I just decided it would be best to be the 'pack mule'. We scaled way back on clothing = lots of hand laundry, and she carried only her toiletries. Her 'suitcase' was about as large and heavy as her purse, and I could even carry that on stairs, etc., when she needed me to. There are many styles of rolling totes (much smaller bags - watch the dimensions - many are billed as under the seat but they aren't. RS's 'Avanti' Regular tote - not rolling - is the max size in my experience.) OR, she could pull the 22" rolling bag with her toiletries (or whatever) and, when necessary, you could much more easily pick up that bag. Then you can bring home souvenirs, although now you are responsible for both bags! Ugh!
All are correct about not carrying a full-size bag on a rolling bag; I've seen small bags bend the handles, then you couldn't collapse them...Plus, you probably won't make it 15' without having to pick it up off the ground! More than a little annoying.
Of course, take into consideration what your mother's limitations are - my mother can pull a bag short distances and carry one OK, but my mother-in-law's arthritis makes it impossible for her to carry a purse, and her arthritic fingers can pull a lightweight bag for a very short distance.
From experience - allow LOTS of time for transfers! This IS a vacation! Dial back on the stress whenever you can. Too-tight transfers with luggage and elderly parents are NOT relaxing. Don't ask. And don't underestimate the stairs; they're your enemy. TAXIS are your friend!!!
I answered your actual (!) question in there somewhere, plus added some unsolicited advice; I hope that's OK. It sounds like perhaps you've travelled before, so you have an idea of how things go (trains, # of stairs everywhere, finding your hotel, etc.). I think my mother's traveling days are over, so I'm happy for the two of you! Have fun planning!