Sorry that came off as negative. It's more or less a very limited amount of time. That's one of the reasons I can't get a "regular job". My wife has an illness we haven't gotten a stable diagnosis for yet, which makes her exhausted all the time, leaving me to watch our 5 children (from teen to baby), which is a full time job in and of itself. The few times I do anything during the day have to be done in tiny windows in which the kids aren't trying to burn down the house and terrorize each other. And I've been consistently getting less sleep than I need because I try to get little amounts of job searching or entrepreneurial work done during late hours. So any time I have to dedicate to doing any of these things, including commenting on HN, is sleep-deprived and rushed.
I just don't understand why your CV is considered too personal, but you are telling all these things.
Although that might be hard, I would recommend to reorganize your life such that you can separate your professional life from your personal/emotional life. Don't get a remote job. Move to wherever you can commute to work. Even if babysitting would take a considerable part of the paycheck, pay for it.
Probable not the comment you wanted to read, but I just wanted to address the elephant in the room. This is not about not finding online gigs. This is deeper than that.
I'm sorry that all of this is happening to your family. You're going through something terrible.
My email is in my profile. If you'd like some editing help, reach out. I can't solve your immediate situation, but maybe I can help strip it from your writing.