I'm really sorry to hear about her health. I hope that she makes a good recovery soon.
Here is what I suggest:
Write to JC Group and include a nice photo of Jackie, in a self-addressed envelope, for him to autograph and send back. It will take a few months, but he will do that. If nothing else you can surprise her with that.
Then I would explain the situation as comprehensively as possible, with emphasis on how much it would mean to her etc. Lay it on thick. Life long fan, his movies have brought her through tough times including this crisis ... etc. etc.
I doubt you'd get Jackie to visit her in hospital or anything like that, but you can ask if it would possible to meet somewhere Jackie is filming or at another event. Although he mostly does this for kids there is always a chance he'd do it for someone else if it is presented in the right way.
Good luck with it. And let us know what happens.