Meanwhile I just emailed somebody in my work's HR department asking about procedures for emergency leave, family emergencies, etc. They have coverage and policies for that, but I'm not sure they cover me in the first six months of employment. We will see -- and I WILL go, if I must, for whatever reason.
EDIT: Talked to Nanc, she said pretty much what Andy said, plus said the hospital is reporting Dad probably won't be in there for "just a week" but might be there over the 60-day hospital stay allowance set by his insurance. WTF?!