@finallyhappyinlife That's great. BUT, you now need to put in writing to both parties (i.e the neighbour and the contractor), your understanding and recollection of todays conversation, what was offered and why she rejected it.
But before you give her the letter, email the contractor with a copy and ask him to confirm he is content that the the letter is a true reflection of his proposed solution. Be aware you are fighting on two fronts here. It will be you she takes to court not the contractor so you need to tie down both the neighbour and the contractor on the fact of how the situation arose and what solution was offered by the contractor because if she sues you, you may have to sue him if you lose the case.
Tell the neighbour that unless her reply includes information to the contrary you will assume all parties are in agreement with what was said, also apologise for the delay. When you send the letter to the neighbour, also copy in the contractor to the final version and ask for an acknowledgement. You need to record todays discussion as they may claim at a later date that something different was said.
In that letter you need to in include photos of her drive beforehand, cover the age/state of it and photos now, explain what the Contractor offered as a solution i.e. repaint it or re-tarmac the surface of the affected part but also point out the potential issues with this as explained by the contractor and make it her choice, so she can't come back later and claim her drive is different shades. Also cover off that the contractor has never had this problem before.
However you might want to check that your contractor has allowed for proper drainage channels.
Acknowledge, enclose and refuse the quotes for the replacement of her drive (stating her figures), saying that you feel this is excessive given the nature of the issue and the age of her drive. Explain you feel an appropriate solution has been offered.
Then give her so many days to respond in writing (say 14 days) so it doesn't drag on.
I'm not legally qualified but this is what I would do.
Good Luck!