I support my mum who lives 100 miles away. She has carers 4x a day and I visit once a week to check on her and do her grocery shopping and any laundry. I ended up dropping from FT to 30 hours a week, visit mum on a Friday and then have a proper weekend with DH. I was burning out doing it on top of a FT position, as well as all the weekday admin, phone calls etc.
I am fortunate to have a fully WFH position with a boss that doesn’t care about core hours as long as the work is getting done, hours are recorded accurately and we meet the clients when they want (her boss went to the gym during the day and blocked out their diary to do it!) So on days where I’ve taken mum to medical appointments I’ve been able to log on and keep work ticking over from her house and make up time during the rest of the week. I recognise though that I’m very lucky in this regard.
Dropping hours was annoying wrt pay and pension contributions but to be honest I’d always vaguely planned that by this age (late 50s) I’d start reducing hours with a view to winding down to retirement in a few years anyway. I think I resent the decision being forced upon me though.
i don’t have children of my own, but one learning I have that works for everyone is to put plans and systems in place so that you are not the default solution to any and all problems. At the start of all of this, any issue would see me hoofing over to mums because I felt the responsibility to fix everything and keep everything nice for her. Now after a near breakdown, counselling and a sertraline prescription, I have some guiding principles. Is this issue something that HAS to be addressed NOW, ie is she injured or does it impact her safety? If so, does it have to be ME that sorts it, or can I call in someone else?
If it’s an issue that does have to be addressed and by me, but not right now, then it waits until the next Friday visit.
if it’s an issue over and above my minimum standards of ensuring mum is safe, warm and fed, then I may address it if I have the time and energy at a time of my choosing. Otherwise I will let it go, and the silver lining of mums dementia is that she’ll forget whatever she was bothered about. Eg she received her usual seed catalogues in the spring and decided she needed me to order her bedding plants for the garden - she has lots of flower beds. I asked her who was going to plant them, water them, deadhead them and dig them up at the end of the year and she just looked at me. I removed the seed catalogues and nothing was said again. 
The result is that mum is fine, the house is in need of attention but it is secure and functions. A cleaner keeps the kitchen and bathroom sanitary, a gardener cuts the grass and keeps on top of the weeds. We’re buggering along just waiting for a crisis to force any kind of change.