I have just had a similar problem in a (non retirement) block of flats. One, share-of-freehold Director took it upon himself to co-ordinate, decisions and liaise with the management company and then failed to organise any AGMs, etc and vetoed any expenditure for common parts, even those required in the lease.
It took several years before we realised why the common parts were looking shabby.
Our solution has been to go back to the paperwork. It should all be in there. (Possible paperwork might include the lease, How people are appointed to the management team, right of consultation etc.)
I assume Bob has been appointed because either:
a) he was a pain so they though it easier to have him on board than not.
b) they are saving money because otherwise they would have to pay someone to do what he does.
I would aim to have as little direct involvement with Bob as possible. One real lesson I have learned in life is that if you are having problems with someone, others probably are as well. It is better to complain about the issue than the person, as they have then to address the issue, rather than palm it off as a personality clash. Let someone else take the flack on the personality problems.
I would then write a letter, which could hint at though not threaten further action. In my case legal action against the problem Director though your unstated threat might be to take it to a body that regulates sheltered or general housing. (Another life lesson don't issue threats unless you are ready to carry them out, but no harm in letting people think you are organised and persistent and could take things further.) In my case once we looked at the Memorandum of Association we realised we could call an AGM, become Directors and make decisions based on a transparent and democratic process. .
Be clear about the problems. Say that the restrictions are diminishing your mother's enjoyment of her otherwise lovely property. (Always be polite and reasonable in any correspondence which may be used again, or read say by an industry body.) Say the lease promises access to the day room, or whatever. Quote any consultation requirements. Say you are writing because it is difficult for a 84 year to be assertive. Ask how these restrictions were put in place, and whether they plan for the lease to be amended to reflect these. Ask generally about the process through which residents are involved in the day to day decision making that involves their access to facilities.
In short, and as clearly as possible sound clear and organised and make the letter sound as if it is a stage one complaint which will be taken further if they don't respond. In short failure to rein in Bob's petty rules will ties them up in more paperwork than they want.
Research governing bodies both for sheltered housing and for property management companies. Google "I want to complain about my management company". Decide what elements of the problem might cause a reason able complaint. (Withdrawal of current access to facilities without consultation etc) Again quote rules and bodies. Google the housing and see whose recommended lists it is on, ie local SS, and if you want to go all guns blazing could suggest you would speak to them as well, given the distress caused to a vulnerable resident from their high handed approach. (Always their approach, not Bob's because they have allowed him to act in their name.)
That should do it!