Oh Sparkle how awful. My ds's health problems aren't anywhere near as bad as your dd's. He has recurrent croup - which has been life threatening on occassions, asthma, and recurrent ear infections - but unfortunately these escalate and cause other problems like taccycardia (sp?).
And how difficult to have two children with medical problems.
This post is gonna be a long one, but I wanted to share my experiences in case it helps. I won't give advice on what you should do, I can only tell you things I try.
Some practical advice the child psych friend gave me was to carefully orchestrate the way the family is reunited after an emergency, so that ds1 could have my undivided attention as quickly as possible.
So for example, if I had been in hospital over night with ds2, I would come home first, and even though I would really want to be with ds1 I would ask my mum/ in laws to hang onto him a bit longer. Then I would get ds2 settled, take a shower, tidy up, have something to eat - take care of myself so I was in the right frame of mind and could unwind from the stress. Then either go to my Mum's or have her come to mine, so that she could take care of ds2, while I was totally focussed on ds1. We would do something simple like play a game,or colour, and eventually he will signal when he wants to talk about what has been happening.
But the scenario above is a luxury to us - we might get to do it 50% of the time, and the rest we just have to muddle through and poor ds1 gets tired, shouty mummy home from the hospital. But it doesn't matter if he can't get that attention every time - just getting it sometimes is helpful.
The thing I am most rubbish at is making the connection between ds1's behaviour and whatever stress is going on in our family. I started posting this thread today at the end of my tether thinking 'why is he being so naughty' and because we have been fortunate enough to go for 6 months without a trip to hospital I forgot that he always does this when me / ds2 gets ill. Poor ds1 has real stress issues around health. And I feel so stupid for not noticing it. Doubt the same applies to you Sparkle as you seem pretty clued up as to the impact this is having on your 5yoDD.
And you sound like you are doing a great job of carving out little chunks of time with dd. With ds1 it is the little things he appreciates - staying up to watch Dr Who when ds2 is in bed, sneaking out with me for a late night trip to the supermarket. I try to do spontaneous stuff with him, and its usually in the evening so ds2 is in bed and dh can be at home.
Initially we were almost 2 families - dh looked after ds1 while I had ds2 because I was more confident with the medical stuff. It has been hard to break that pattern but I think we are getting there.
And one last thing - someone mentioned it on another thread I'm on - don't forget how angry the healthy child can get about the poorly child - I have lost count of the number of times ds1 has punched ds2's ear since he sees it as the route of all evil. Your dd may not be angry, or she may be seething underneath and scared to show it. Ds1 likes to tell his toys how much he hates 'mummy's cough', or 'ds2's cough' - after a tip from another MN I'm gonna try some art therapy with him - get him to draw all the nasty things.
I hope that helps a bit. Please don't forget yourself in the mayhem.