Are you sure your mum is as fit and healthy as you think?
Sometimes people who seem fine in their own environment are actually pretty useless with things like public transport links and large crowds.
I ask because my mum seems to be competent in her own area, but when out and about, always talks to the weirdo, and seems totally stressed with any event where she has to go it alone. I drop her off to the airport for eg and have to remind her to listen out for announcements, to watch the flights info boards and not just to follow some nice looking couple to their gate (as she has done before).
Maybe she's losing her hearing, and eye sight isn't as well as you think?
Otoh, she may well be someone who is used to all the attention, and being looked after, and she doesn't think for one second about you and the inconvenience to you and your family of meeting her.
Dragging a toddler around London sounds like a barrel of laughs....
Does she have a mobile? Could she phone you when she gets off her train, and you could talk her through the tube? Is there any middle ground?
I would think someone in their 60s would be fine, unless she's frail and carrying a huge case.
Btw, I have such a dependent but hale and hearty mother, and over the years I've bent over backwards, and put myself out financially for her- not sure if you feel like this fits your scenario, but my mother doesn't even notice the effort other people go to help her out.
My dad died 20 years ago and as I'm the only family in the country, the burden falls to me. It grates, and I go no contact when I've had enough babysitting her. She also has a fantasy that I'll look after her when she gets old and frail, and she'll move in with us.