I'm not sure I understand your time frames above, but if they mean what I think they mean, you're totally off on your estimates, both national parks are much farther from Seattle than you've indicated.

Some of the gateway towns to the Olympic National Park (not Olympia as you have above) include Port Angeles, Forks, Sequim, and Hoodsport. Those are just the close towns, driving up into the park adds additional time. Port Angeles is at least 2 1/2 hours from Seattle, including a ferry ride. Forks is 4 hours, including a ferry ride, Sequim is 2 hours including a ferry ride. Hoodsport is 2 hours (assuming light traffic on I-5) with no ferry ride. Depending on how you time your trip, you may wait 30 minutes to 2 hours or more to get on a ferry. There's no way you're going to get to a park entrance in an hour from Seattle.

There are similar problems accessing the North Cascades National Park. Your most likely route is to drive up I-5 to the North Cascades Highway (Route 20). From Seattle, Diablo is 2 1/2 hours just to get you into the park. If you want to come into the southern end, drive to Chelan (3 1/2 hours from Seattle) and take a 2 - 4 hour boat ride up to Steheken where you'll have to hike in. Unless you're just planning a quick drive-by viewing, I wouldn't try to do either park from Seattle in the time frame that you seem to have.

Burlington is right at the intersection of I-5 and Hwy 20, so if you're computing your time from there, 2 hours would give you time to drive up Hwy 20 pretty far into the park, possibly to Ross Lake and back. It's a spectacular drive, well recommended if you haven't done it before. The Park Headquarters is on Hwy 20 on the left just as you leave Burlington, stop and get maps and information before you head out.

Another possible day trip, since you're going to be in Burlington, is to drive 30 minutes west to the ferry landing in Anacortes, park your car, and take the ferry to the San Juan Islands or to British Columbia. Walking on ensures that you won't have to wait in line to get on or get back. The ride out is beautiful, Friday Harbor and Victoria are both very walkable once you land. Check the schedules since not all of the ferries go to BC.