You and your GD sound lovely. It’s clear you’re desperate to alleviate her desperation, worry, disappointment, stress.
To me it’s not about favouritism or equality or fairness. It’s about how you feel seeing someone you love, so upset.
As such, I don’t think that giving GD £10,000 for one round of IVF, especially (but not just because) if you don’t have any left for other grandchildren, is foolhardy.
IVF has, if all the stars align and everything is in everyone’s favour, all throughout the process, an approximately 32% chance of resulting in a healthy birth (generalising and simplifying massively). Those odds wouldn’t be good enough for me given you can’t afford this without consequences. That means a 68% chance of spending that money and everyone ultimately being in a worse position: just as upset, poorer, even more helpless, with nothing left for the others.
Three of your grandchildren are teenagers. Who knows what the future holds. Their needs, or one of them, even 6 months from now could be far, far greater than this GD’s. Bereavement; disability; redundancy with mouths to feed. What about your own needs and care as you age?
Money isn’t the answer to this situation. You feel like it is and you want to help so very much, but money very probably won’t solve this.
In your shoes I would extend love, sympathy, understanding. I would let GD and her husband deal with the cards fate has dealt them (for now), as best they can. Many many couples struggle with infertility. Many go on to say it was a dire time but they move on and end up in a new place, content.
If need be, you can assist with counselling or therapy.