u/Flaky-Soup

I'm looking to DIY a dog wash/mop sink. How can I make this work with my current setup? Do I need to leave an access to the cleanout? If so what would be the best way to access since there will be a tall cabinet between the shower and the dryer.

Also, would I need to be able to access the valves, or would the last picture be a good solution to the valve issue?