OP - get a letter from your consultant. I can't blame you for being embarrassed to go back on the bus but these bullies shouldn't be allowed to get away from it.
I don't think it's actually a legal requirement to fold buggies if a wheelchair wishes to board. AFAIK the legal requirement is for compliance with the equality act by the bus company. Notices on the bus, statements in the conditions of carriage etc do not constitute legal requirements and are breaking the law if they violate the equality act.
The Equality Act 2010 States
You're disabled under the Equality Act 2010 if you have a physical or mental impairment that has a "substantial" and "long-term" negative effect on your ability to do normal daily activities.
"long-term" means 12 months or more
where an impairment is subject to treatment or correction, the impairment is to be treated as having a substantial adverse effect if, but for the treatment or correction
I'd certainly describe breathing as a normal daily activity. I don't know how long the OP's DD's condition is likely to last although if the condition is likely to last for over 12 months but improve due to treatment it still constitutes a disability. A broken leg is unlikely to count.
Discrimination can come in one of the following forms:
direct discrimination - treating someone with a protected characteristic less favourably than others
indirect discrimination - putting rules or arrangements in place that apply to everyone, but that put someone with a protected characteristic at an unfair disadvantage
harassment - unwanted behaviour linked to a protected characteristic that violates someone's dignity or creates an offensive environment for them
victimisation - treating someone unfairly because they've complained about discrimination or harassment
It can be lawful to have specific rules or arrangements in place, as long as they can be justified.
The policy of expecting buggies to be folded puts the OP and her DD at an unfair disadvantage in my book so is likely to constitute indirect discrimination. I'd question whether 'the space is intended for a wheelchair' is valid justification. What gives the person or people who designed the vehicle (or even the minister for transport) the right to say that a wheelchair user's journey is more important than the OP's journey AND possibly her DD's heath??? Waiting in the cold, not getting home in time to change oxygen bottle etc could be potentially life threatening.