Best route to take in Hokkaido

I intend to visit these places, hakodate, noborobeitsu, sapporo, otaru, furano and
Biel,
My preferred mode of transport is a mix of rail and car. My family will flying in to sapporo on 20 jun and leaving on 28 jun. Appreciate advice on route and also attractions in these places.

Where are you flying in to?
Flying out off?

Or are you taking a ferry? Or a train?

Based on days and locations
Fly into hakodate
Spend one night

Drive to noborobeitsu
Stopping at Lake toya along the way
If you trust your skills, drive all the way to Nobori, if not stay a night at Toya
Night at Nobori... onsen

Drive to furano and Bei
Spend three nights here
One day for transit, then a full day each for both places

Spend the rest of the nights at Sapporo
Otaru requires half a day

I personally think you have too much time in Sapporo, and would recommend a side trip from Furano to Daisetuzan national park. Beautiful mountain and even better in summer. Hot springs and nature lovers apply.

Sounkyo gorge is one of the places to stay the night.