One thing you could consider is rather than focusing on a specific challenge to encourage others to donate as a one-off, is how you could have a similar (or larger) impact over the longer term by doing some other things yourself.
I've done this with a small local cancer charity that provided real practical support to me going through my cancer treatment. I made sure to nominate them where possible as my charity of choice for auto-donations - like Amazon Smile. M&S and other retailers have similar options too.
I purchase things like Christmas cards, calendars, diaries, little stocking fillers from their online shop. I use gift aid. I've made a provision for the charity in my will.
I also point people to the charity's amazon wish list and/or their donation page when asked what Christmas or Birthday presents I might like. I find people are much more receptive to this, and follow through with a donation, rather than by being just another person on their timeline doing a sponsored challenge.
A friend of mine does a lot of e-baying. She gives a small, fixed percentage of each sale to a charity she supports. As a percentage on an individual sale it is not much, hardly noticeable, but over time it has added up to a decent and generous amount.
Finally, when the Covid restrictions are finally over, I'm intending on doing a car-boot to off-load the results of a massive de-clutter and life edit with the proceeds going to my cancer charity.
Good luck with what you decide, and I hope things are looking brighter for your family moving forward.