Its not just young mums - there can be some pretty inconsiderate usage of mobile scooters driven by elderly users as well!
But they're not using stairs or lifts on them I imagine, however the point is clear but, some of these mobile scooter users have perhaps never driven cars, so have no understanding of road rules, and this should be addressed by the government and is a very valid, but different, argument.
The staircase that Silver has described sounds like it's in a pretty old sort of shop where human traffic once flowed nicely and with thought for others and, from her description, it was just one mother with one child who was being over-indulgent with her child's "accomplishments" instead of gently urging the child for respect for other users of the stairway, instead of causing a back-up of traffic and yes, this achievement should be shown with the stairs at home, but instilled some consideration in the child whilst out shopping.
As for buses, I've no clue, as I haven't used one in over 40 years, but what has been described sounds like an horrendous way to travel. I don't see why lifts etc should "give way" to buggies and wheelchairs though. The people occupying them are hopefully sitting in comfort, whereas perhaps much older people who can't stand for any length of time would find it most uncomfortable waiting for 7 - 10 minutes. There was a time when a lift was totally out of the question for me and I'd climb up to 10 flights of stairs when I was able rather than wait for a lift as I'm claustrophobic but sadly, I can no longer do that, so I take the lift at my surgery up to the first floor, and I hate it, but I've had to overcome that fear. However, that is of no consequence and was just an aside to the content of the thread.
I would indeed give preference to a wheelchair user over a buggy user. A person in a wheelchair may have been born to it or, through unfortunate circumstances it became necessary due to illness later in life. However, if a person chooses to have a child, that is by choice so in my eyes their rights diminish. Sorry if that sounds harsh, but those are my thoughts.