I understand why you are reluctant to go, but I think you should.
Even though your dad's on the mend, he could still be in the hospital for some time. Make an appointment with the doctor. I'm sure that you have done this anyway, as some discussion will have to take place about your Dad's discharge from hospital. Ask their opinion about going away.
My mum's whose 85 spent over a month in hospital with a chest infection. She thought, as did my sister and brothers that she would only be in for a couple of days She was discharged over 2 weeks ago and some days are better than others, although her spirits are good.
My journey to see her can take anywhere from 6-10 hours and I see her pretty regularly. I spent the first 10 days in the hospital and came back when she was discharged and stayed with her at home for another week. Other family members (2 brothers and a sister) were with her when I wasn't. Mum lives on her own and we try and go and see her as often as possible, which means there is usually someone there most weekends, which is pretty good considering all of us live some distance away; my sister a 100 miles away and my brothers and I are in London. Although I have to say that my sister too, does more than her share of the care.
As I live so far away and it's heartbreaking to say goodbye, as I am never sure if it's the last time. I can't afford to think what might happen if I am not there. However, I have to live my other life too. I know my brother and sister feel this too. My DP and DS (10) have been wonderful, and I need to look after them too. It's hard juggling and at times I'm exhausted taking everyone into account.
This holiday has been booked for some time. I'm sure you need the break. Caring for parents while hugely rewarding is very draining and there will be lots to do when your dad comes out of hospital.
Your daughter is probably scared. It's so painful to see someone you love ill and difficult at 20 to deal with the issue of mortality. Could your sister stay with her until you came back from your holiday and take over at the hospital? Could you talk to your Dad about the holiday and find out his opinion?
Again, I would advise speak to your Dad's doctor. They can give the best advice.
I do empathize. I came back to London on the 16th Dec and will not see my mum again until the 5th Jan, but I have had a lovely Christmas holiday with my boys, just as my mum wanted.