How do you set boundaries with the elderly?

You can teach a child about setting and respecting boundaries. With a very old person who has declining cerebral functions, you will waste your time it attempting to do the same thing.

"Tell me what I can do, Mom".

If she has an actionable plan for how to solve the problem of your brother or her health, let her put that on the table.

BUT if she is just verbally abusing you, absent yourself from her presence until she calms down. Or just hold her hand, not reacting, until she calms down.

She may need a visit to a geriatric psychiatrist; meds for depression, anxiety and agitation work.

At 97 it is more likely that she also has dementia, which manifests as increasing stubbornness, negativity and paranoia. It is pointless to try to set boundaries and expect someone with cognitive decline and possibly also memory issues to be able to handle new boundaries.

It would help everyone the most to take her to her physician for a cognitive/memory test and maybe also check for a UTI. Then find some of the very excellent educational resources online to learn about dementia and how to better engage with people so that you can have more peaceful and production interactions with them.

Well at her age and condition, I don't know how far to go with setting boundaries. Is she acting angry AT you? Or just venting and complaining to you type of meltdown? Look up grey rock and see if you can just let it wash over you and not engage. Just let her vent and let it go in one ear and out the other. You could cut your visit super short when she's like this if it's intolerable (which would be understandable). Tell her that you see and understand that she's upset but you have an appointment that you really need to get to. And then leave.