I was in the same boat.
My father was diagnosed and as he lives 150 miles from me and needed help I went down there. The trouble was I only had 2 days left.
My boss said I could take days from next years holiday (which I thought was a bit unfair), so I looked on the HR website as I would need more time off when he goes for the op and recovers.
Lo and Behold, hidden away at the bottom was a section on special leave.
I'm entitled to 17 days off a year to care for a sick relative plus 5 days off 5 times a year for a family emergency.
Presented this to my boss, mentioned it to HR and they are now letting me use this.
I work for BT. A large company I know, so I guess it depends who you work for.
Also my Union have backed me and my boss is aware of this as well.
Good Luck and all the best.