I think you're tying yourself in knots and that its not helpful for you or anybody else, so please, be kinder to yourself and stop it.
They made a request, You feel sympathetic to them, and would comply if you could, but you can't. £30k means it's an absolute no go.
You have gone well over and above to offer her an office to work from. She can make use of that, she can find the quietest place in her own home and wear noise cancelling headphones, or she could find a coffee shop, town library, friend or family's house, paid co-working space, or she could shift her day around to work more in the evenings etc etc. It's her family's job to help her to find the best solution to make the most of it, not yours.
Your job is to deliver the news sympathetically but without any wriggle room. "Just to let you know that we have looked into it and unfortunately delaying the works at this stage is just not going to be possible. We do recognise that it's not the outcome that you would wish for, and we are truly sorry for any disruption. We will ensure that any noise doesn't start before X and doesn't continue beyond Y. The offer for X to work at the office is still open, do let us know if she'd like to come and give it a try. Wishing you all the best, X and Y."
If you wanted to, you could gift them a £50 or £100 Amazon voucher "for study materials including anything that helps to mitigate the noise" as a goodwill gesture.
I think it's important that you DO say no to at least some of their requests. The bike rust thing one sounds full on ridiculous, and they would be being VERY unreasonable if they didn't accept you declining to incur £30k additional costs.
But please, stop beating yourself up. You wouldn't have chosen this situation, but here you all are in it and you must all just do your best to get on with it. And dare I say it, but young people could do with developing a bit of resilience. It isn't the worst adversity for her to overcome.