I also never recommend Vancouver Island as a day trip. Always do at least one overnight. I have rented one way cars, MANY times, using Avis, Alamo, National, Budget. I go with the cheapest. There is also Hertz. You want downtown Vancouver NOT the airport. I most always walk to Canada Place, after dropping off/picking up bags.
I also would not recommend you go to Vancouver, then back track to Vancouver Island. Take the ferry out of Ancortes, or Port Angels, then from Vancouver Island via Tsawwassen to Vancouver.