Just laid out the route using Cheyenne as the start.
Longest day-to SLC. SLC to Reno or Tahoe. Reno to SF.
The trip up 101 from SF takes you to Eureka in about 5.5 hours drive time. Spend an hour or 2 in Redwood NP.
Next day north on 101 to somplace on the Oregon coast possibly as far as Newport. See the major aquarium just south of Newport.
Decide which route from Newport to Seattle east on US 20 and north on I-5 or north on 101 over the big Astoria bridge.
How are you getting back to WY? Consider I-84 through Boise with a stop or 2 in the Columbia Gorge.

> is this too much driving?

You'll be able to make this drive in five days.

> Or ample time to enjoy the coast?

You just won't have enough time to adequately enjoy anything along the way.

I could give a five-day itinerary north from San Francisco, but you wouldn't get to Oregon.

Or a one week itinerary in Oregon.

Or a five-day itinerary from Portland to Seattle.

But doing five days from San Francisco to Seattle means you'll often be saying, "If it's Tuesday, this must be Crater Lake."

Two days in Oregon is better than no days in Oregon.
I asked about your return route. Your choices include the Columbia Gorge, Bend/Mt. Bachelor, or Crater Lake.
What are you seeing in the Seattle area?

We've done it in 5 days with selective sight-weeing: the Redwoods on highway 101 (Avenue of the Giants, the Rockefeller Grove), but we usually leave the coast at Crescent City to go to Crater Lake. From there we drive up on the eastern side of the Cascades to approach Mt. St. Helens and Rainier from the east and south east.

But since you are from Wyoming, the Oregon coast might be more interesting for you. If so, the Oregon Dunes are a place to visit. I would cut over toward Portland and go one to Seattle. I do not find the coast between Tillamook and Astoria particularly attractive.

We usually camp along the way, generally in National Forest campgrounds. For California State Parks, reservations are advised.

One issue to keep in mind for the Oregon coast in summer..due to traffic 45 MPH is the average speed.
Eureka to Bandon is 4 hrs. this part of coast is" rustic" not glitzy; on to Newport is 2 1/2 - 3 hrs.: to Tillamook is "inland"-1 1/2 hrs. (great cheese and ice cream) then to Astoria is about 2 hrs. because Cannon Beach and Seaside are very popular.
These times do not include stops for food or walk the beaches...
From Astoria we always went East toward Portland and hooked into I-5 to Seattle.
as you might have guessed we made this trip many times, last one was 4-5 years ago so there could be some changes.
Also useful on this site is to do a "search' on Oregon coast, Seattle etc. do pay attention to the dates of the replies on search.
Also--almost any lodging on the coast --especially weekends- requires reservations!
I am sure some one will post a question as to what you are interested in seeing..especially your boys..
Lots to do and see in Seattle.
Happy trails

sight-weeing = sight-seeing

Our favorite places to stay on the Oregon coast are Bandon, Yachats, Newport, and Cannon Beach.

The best ocean views from Highway 101 are from Brookings to Port Orford and from just north of Florence to Lincoln City.

Enjoy, HTTY

You might consider bagging going up the Cal Coast - and leaving SF early - and getting up to say Crater Lake (8 hour drive?) one of the 7 Natural Wonders of the world) - and stay there - or at the Lodge at nearby Diamond Lake. http://www.diamondlake.net/

You could then take a very scenic drive along the North Umpqua river over to the Oregon Coast and then head north.

And outside of Portland - about an hour to the east - is one of our favorite places - Timberline up at Mt. Hood. From there - you could leave in the morning, drive up to Hood River - along the Gorge and see the waterfalls (stop especially at Multnomah) and then from there - it's about 3 hours to Seattle. http://www.timberlinelodge.com/

The route I was considering was up Interstate 5 - and then - at Reddint take one of two options to Crater Lake: On Interstaste 5 up through Medford or up 5 as far as Weed and then take 97 to Klamath Falls and along 30 mile long Klamath Lake to Crater Lake.