I think you are being hugely unreasonable.
At 92 I imagine that your Mil has been to the chiropody clinic many times before, she knows the layout, she knows the staff, she feels secure navigating her way around the premises, knows where the entrances are, the reception desk, the toilets etc. She probably felt confident to deal with the appointment on her own.
Whereas hospitals these days are confusing places for many people. Everyone is masked, communication can be difficult , new one way systems are set up ,it might not be particularly clear where you need to go, or indeed where you are allowed to go . Even if she has attended outpatient clinics there before she will be aware that things might not be the same.
Ditto the COVID vaccination, very few of us have had these, we don’t know the protocols involved, but we do know that it is not likely to be as simple a process as turning up to your go for a blood test or your flu jab.
I am sure the OPs husband would have been only to pleased to accompany his mother if he was able to , but he can’t. Sad that the Op doesn’t feel able to step into his shoes and show some compassion.