I homeschool and my husband works 6 days a week, so my weekends tend to be just as busy or busier than my week. When I set up my weeklies in my bullet journal, I give every day the same amount of room. But I tend to do more of a dashboard weekly, with tiny boxes to write events and dinner plans in, then a lot of free space for daily notes as the week goes on. I don't normally have a daily page when I'm making my own. But I don't see how you could skip a daily with what you're trying to achieve.
My only recommendation would be to split the week over the two pages, and give the dotted notes section the same amount of space as a day. So it would give you symmetrical pages with 4 spaces on each page. I can provide pictures of my personal planner where I've done that, though it obviously wouldn't have the quest stuff on the page.