I've done huge amounts to reassure them but they are always fixated on the dailymail headlines.
Perhaps stop.
If your mum is rather 'dramatic' then this is the way you have been expected to behave - your Mum gets upset about something and everyone makes huge effort to calm her down and "help her cope" with whatever has caused the upset. You all work round it and change your behaviour to minimise her upset.
So don't.
As PP have said, just agree with her, say you are sure she knows best.
Don't try to talk her round.
Don't try to find a way for her to see the DGC in a way that fits in with her restrictions.
Don't go out of your way to schedule multiple facetime calls or special trips to wave from the garden (this would be for her benefit, not the DCs and may well upset them).
Just agree and say you'll sure she knows best.
Then get on with your life, accept she's choosing to miss out. And most importantly, remember your father is also choosing this life, he is not a child, he could just refuse to stick to her rules, he could tell her she's being silly. He is obviously getting something from enabling the drama around her health. (Many men like having a wife who's 'delicate' who needs to be looked after.)
Step back and get on without them in your life for a year.
When everyone isn't fussing around her, and she can see everyone else is happily getting on with life without her, she might realise she's being silly.
(Have they taken early retirement or is your Dad expected to give up work? Again, don't engage in discussions about this, don't even bring it up as an issue, it's their problem to fix, nothing to do with you.)