It sounds to me that you've all got too much on your plates and GS's injury has highlighted that you're all on the edge. You and your husband have medical issues of your own to deal with, plus elderly parents in poor heath to support plus a DD who has a demanding job and two DC to cope with (one a teenager with the angst which goes with that age). You are in the Sandwich Generation.
The hitch in your arrangements is that the emergency contact issue should have been dealt with before now. But you've all been too tied up with just coping day to day. I remember the guilt of not being there for my DH who had health problems and needed me, at the same time as taking my DF to hospital appointments for cancer treatment, (supporting my DM emotionally) and also collect DGD from school when she'd been sick and they didn't want her in school (DD had no transport).
You cannot do it all. Just remember the airplane instruction that you must fit your own oxygen mask before helping others. Yes, I would have gone to fetch DGS, and felt guilt at upsetting DH and the meal we'd so looked forward to, but that doesn't mean I should have gone. And it doesn't mean that I'd have been safe to drive while over-stressed and in a hurry.
What's done is done. Hopefully your DD will come round soon and realise the situation.