Ooo! A time limit!!
You are between a rock and a hard place.
We used to drive Seattle to Milwaukee, WI and back in two weeks (2K miles both ways). We made the best time we could going, and then took our time coming back and visiting the things that interested us on the way. However you don't have that luxury of coming back the same way. Of course we had no trailer at that time, but we did have 5 kids.
I make your trip to be about 2200 miles,
The only secondary roads you would travel would be between PDX and SFO the rest is freeway. Note: Towing speed limits in CA and OR are 55mph.
Here is what I would do: Drive with all alacrity to PDX. This is your longest leg and it is best to have it behind you. Then tour down the coast using the various suggestions from this site and then return via freeway SFO-SLC. 700 miles you should be able to make in two days. That would leave 9 days for the 'touring' part of the trip. At any rate, I would plan on 3 days for SFO-SLC..
Only you can decide what you want to see along the touring route.
Just before arriving at PDX you should visit Multnomah Falls.
"The falls drops in two major steps, split into an upper falls of 542 feet (165 m) and a lower falls of 69 feet (21 m), with a gradual 9 foot (3 m) drop in elevation between the two, so the total height of the waterfall is conventionally given as 620 feet (189 m)."
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