The scooter was quite obviously allowed on the train. By the mere fact it was there. Tanyalee Davis received assistance boarding at Plymouth. It's clear from her videos (there are others on her YouTube channel) that the scooter is small enough to manoeuvre on a Mk3 carriage.
By her own words she is a regular rail traveller in the UK using said scooter.
That GWR had a scooter policy is of little consequence. She hasn't broken any law in being in her scooter aboard the GWR train. GWR's scooter policy doesn't give their staff carte blanche to move a disabled person from a disabled space. GWR's scooter policy doesn't give their staff the right to humiliate a disabled person over the public address. GWR's scooter policy doesn't give their staff the right to threaten disabled people with police attendance or being thrown off the train.
To address the possible 'protected characteristics' of the mother and baby. Yes, she may well have been afforded some protection under the Equality Act if her child is under 26 weeks old. Not for a broken limb, likely to heal within 12 months, though.
That doesn't though give her rights that trump those of a disabled person. In this case, on a train with only one disabled space available, unreserved for the entire journey (yes, I've checked both those points) it's first come first served.
Until I see or hear compelling evidence to the contrary, I maintain my stance on the Train Manager's continued employment.