Lulu,
So very sorry for the bad news your family received. Life has a way of throwing curve balls.
But, I want to share some encouraging thoughts:
My father-in-law was given similar news about 5 years ago (lung cancer....occupational hazard). We thought that would be his last Thanksgiving, Christmas, Birthday, etc. He had considered pallative care, but remarkably without receiving treatment, the cancer has not spread and his quality of life is remarkable. He's active in his community and he's even traveled a bit. He feels great....better than before receiving the diagnosis. He does not look sick at all; looks like an incredibly fit, healthy, happy 86 year old. Likely he will someday die WITH the cancer rather than FROM the cancer.......but likely not anytime soon!
So, maybe your family will be as fortunate.
I would encourage you to not change the plans for your trip. If everything but your airline can be canceled without penalty, there is no reason to cancel anything now. The airline penalties will be the same if you make a change now or if you do it the day before. Wait...see how it goes. And, if by freeing up the seats on a otherwise packed plane helps the airline, who knows, they may let you make a change without a penalty (so they can sell the seats for higher fares). Or there may be a huge hurricane that happens the day before your travel, and the airline may be waiving the change penalties anyway. Or, the airline may notify you in a few weeks about a change in your itinerary (that happens a lot), and then YOU will be in a position to negotiate a change. Things have a way of working out in life sometimes.
From which company did you purchase your travel insurance? Usually, if you have to file a claim, you can sign a waiver with the travel insurance company (basically saying you won't use the tickets) and you can get a full refund under your policy. Also, usually the illness/but definitely death of a family member is a covered cause, should you need to cancel.
But, worst case scenario, you will be out the change fee for the airlines, and you can then rebook the trip for a later date typically within a year by receiving a credit voucher from the airline.
See how your father is doing closer to your travel dates, and make the decision then.
It may seem a little strange, but I even heard of a family in our neighborhood who told the funeral home "to put grandpa on ice" until they returned from their big annual family ski trip. But, if your mother is still alive, she'd likely need some comfort/help/reassurance immediately after his death.
I wish your father comfort, strength for your family, and many happy times ahead.
And, if arrangements are not pre-done, might be helpful to predetermine details for when that difficult time comes. Preparing readings for the memorial, selecting songs, photos for a celebration of life, writing the obit, etc. Sometimes it's like taking an umbrella, if one is all prepared, the storm just does not come!!!
And, if your father is aware of your trip, and he if whispers: "Go...enjoy." that would be a lovely gift :)