Upvote:2
You only need to apply for an ESTA once, an ESTA is valid for 2 years before you have to apply for a new one.
Your ESTA just authorises you to travel to the United States. When you get to the border you will tell them your connecting to Vancouver and they will enter you on the Visa Waiver Program(VWP).
When you leave Vancouver your ESTA will allow you to fly into the USA again. When you enter the USA the second time you will tell them you are coming on holiday for a week, they will again enter you on the VWP.
On the ESTA form for address in the USA I would just put the airport you are using to transit to Vancouver.
You may want to read more about ESTA and the VWP here.