You can get from Vancouver to Butchart on BC Ferries with the car. The car will cost $51.25 one way. This excludes the driver and pax. Each adult in the car costs $15.50 one way. Children 5-11 y.o. cost $7.75. Younger = free.
You don't have to come back to Tsawwassen to head for Seattle. There are two other choices to get to WA State. One is WA State Ferry that leaves from Sidney, quite close to Butchart and arrives at Anacortes, having gone through the San Juan Islands. The other choice is the Black Ball Coho which leaves from downtown Victoria to Port Angeles on the Olympic Peninsula.
You will need to allow approx 4 hours one way from downtown Vancouver to Butchart. Here's the map for getting to Butchart and then taking the WA State Ferry from Sidney to Anacortes:
Here's a map for getting from Butchart to Victoria, to Port Angeles, to Seattle:
Either way you will be taking two ferries, either BC Ferries twice or one BC Ferry and then a second ferry out of Victoria. The driving times and distances are outlined in the left sidebar of the maps linked above. You can check the American ferry schedules here. Reservations are a good idea as the American ships are smaller than BC Ferries. You also have to allow an hour in advance of sailing for US Customs pre-clearance:
With 5 hours, and I'm not sure you will even have that after a 4 hour journey to the Island, you might want to have a look at this new service. How are you figuring 5 hours? It's a HOHO bus that visits 6 attractions, including Butchart on the Saanich Peninsula. It picks up at Swartz Bay ferry terminal and drops off there too. I can't speak to it, but CVS Shuttle the company is well established in Vic, there will be no reviews yet, it includes a transfer at Butchart to its other shuttle to downtown Victoria.
The brochure: http://www.peninsulashuttle.ca/
From the parent company website: www.cvscruisevictoria.com/PAC/indexpac.html
Bottom line. Car you are free to do things the way you want. No car, you are tied to more than one transportation schedule. I just can't fathom how a 4 hour journey to Vic, a 4.5 hour journey to Seattle + plus 5 hours in Victoria is going to work.