I read your subject, then your first paragrapgh, so far so good, but then you had to ask about your daughter.
For you as a citizen you can stay out of the country for as long as you'd like. However, I don't get it about your daughter, she is an adult already. I am not an expert about that. I think it is better if you are a citizen and your adult offspring is unmarried. I think it gets harder or impossible for married offspring. Bottom line, you can go out of the U.S. for as long as you like after you become a citizen, but I don't know about your daughter's application, it is simply out of my knowledge area, she might be fine, but I don't know. This would be the wrong forum to ask for this question, I would suggest to ask this question in a family green card forum.
By the way, how close are you to get citizenship? I am sorry if I sound too blunt, but if she is too sick and you still haven't naturalized isn't it possible she might die (or should I use the "pass away" euphemism) before you naturalize?
I know that many immigrants are confronted with this kind of impossible situations day in and day out and I would hope congress or USCIS would have more mercy, but it is just that there are times in your immigration journey when one unfortunately cannot afford to leave the U.S. even for certain family emergencies. It sounds sad and inhumane, but that is the state of things in this bureaucracy.
DO : San Jose
11/28/2006 : Mailed
12/04/2006 : PD (and Receive Date)
12/05/2006 : Check cashed
12/11/2006 : Notice Date (Received on the 14th)
12/22/2006 : FP ND
01/09/2007 : FP Appt
12/29/2006 : FP Done. Walk-In
07/17/2007 : Interview (ND May 17)
08/22/2007 : Oath (Received Jul 26, issued on the 23d, mailed on 24th)
08/23/2007 : Applied N-600 and Expedited Passport
09/06/2007 : Passport received
08/20/2008 : Sent N-565 (Approved Feb 17, 2009)