I mentioned that you should consider if you want your support system on the same infra as the system that could be an issue. Creates a catch 22, but you could look at HESK. Simple, email flow. It's SysAids free thing. It itself I don't know if it's dockerized, but you pull a simple nginx/apache+php install, setup a db container (it may support sqlite, can't remember) and you're golden.
Don't overlook the OS default options. Quick Assist in Windows 10+, Facetime can screenshare in MacOS/iOS devices. Not sure if there's an android comparable.
If you are running chromebooks or linux for family users then it makes sense to install a client.
In my experience, this mitigates the issue of you managing software on devices and allows you to support even new/remote devices.
This assumes you're only doing ad-hoc support, and not making sure they are applying windows updates or maintaining other software updates on their behalf (which I do for my parents every 4th of July and Christmas gathering, everyone else can deal with their own).
Zammad may tick most of the boxes, though I'm not intimiately familiar with osTickets collaborator fuction. Zammad if others are on To/CC lines then when you "reply all" they stick with the ticket. THough in my install I see that it's not easy to see who's on a ticket. I'd be happy to let you be-bop around my home install sometime as a demo.
It has organizations and they can be selectively shared. Though, I think it's "all users can see all tickets within organization" or "all users can only see their tickets". Not a "users can see theirs, managers only can see organization".
It's a very polished interface, includes SSO integrations, and can be white labeled.
Has email scraping, form submission, and API/webhooks, and some workflow automation funciton.
It also has good agent-side support to have standardized signatures, response templates, and visibility on activity and some OK reporting.