YA time travel book where a family skips forward through time

Question

I read this book sometime in 2002/3 at school in Australia. From what I can remember of the plot:

• It's set in the future
• The main character is a female, and I think either her mum or dad works with the government (I'm pretty sure it's her dad though)
• There's a device that allows them to skip or jump through time
• Her dad is wanted by the government because of the device
• The family has to go on the run
• The main character's sister falls in love with someone from another time and they leave her behind (for some reason I'm getting canoe/water association)
• The mother dies (I think of cancer?) and they bury her in another time
• The main character and her dad continue to jump through time to the last days of the Earth

Answer 1

Could it be "Stuck in Fast Forward" or "The Hunger of Time" by Damien Broderick & Rory Barnes?

From a review of "Stuck in Fast Forward":

Convinced that a plague is about to bring about the end of the world, Natalie's dad tries to pack his family into a time machine that he has built in the garage - a bubble in space-time called a "vacuole" that will allow them to skip into the future.

They're forced to leave the sister behind:

Things go slightly awry when Nat's kid sister Fiona refuses to go, snatching the family dog Ferdinand and running away at the last moment.

On the other side of the portal:

When the family emerge from the vacuole a few minutes later they find that more than a year has passed, and that Fiona is now a harder and wiser young woman having lived through the plague.

Realising that things are not yet safe enough, the family jumps into the future, stopping to pick up a cute guy along the way, before jumping again and again through time in search of a future they can live in.

"The Hunger Of Time" is basically an expanded edition of the first book. According to the authors it's also significantly darker in tone. Haven't read the first book, so I can't comment on that. But I did spot some (superficial) changes. The sister's name has been altered from Fiona to Suzanna. And the dad's moved on from Donald to Hugh!

An extract from "The Hunger Of Time" shortly after Grace (the mom) dies:

We could not bear to leave Mom’s body in the multiple landscapes of 5445. Weeping, we carried her into the vacuole and laid her on a foam rubber mattress. After some hours—or it might have been days, so far as I could tell in my grief—Hugh activated the time change and brought her with us through the green flash.

Natalie bumps into Suzanna/Zanna in yet another future timeline:

Barong and his consort lived in a kind of floating palace in what had once been the South Pacific but was now, naturally, the North Pacific. He and Zanna had been married seven years earlier with all due pomp and ceremony...

Go through a preview the book here or here.