The well-being of our elderly mother is being affected by all the anxiety. But she is in denial of the situation and evasively refuses to discuss my siblings past mental health history and hospitalization
about 20 years ago for what I suspect was at least 'self harming'.

Responding to what I think is the central point in the opening post--

Assisting your mother's mental health can be done without going into the past issues and without arguing with her denial-pattern. You could just think about what she needs and be sure she's got plenty of it, such as breaktime/distraction from stressy stuff.

There will usually be at least one healthy-minded person in an individual's circle who can provide some leadership on that, and any healthy good stuff goes a HUGE way toward the wellness of the person concerned. You may not know who that person is, but mum probably knows who can be counted on to take a light approach to the situation in the whole mix of the people surrounding her.

A professional can consult with fam members to identify what level of help/support/encouragement is needed by mum and/or all parties. The focus, in other words, needs to be on the system, not just the part that appears most broken.

~Susan