I want to say for the red stains, Red Relief by pros choice. I think on the bottle it tells you how to use it on natural fibers like wool and cotton. If you are going to use an iron with the Red Relief, make sure it's set for cotton on the dial.
I also like to clean cotton with peroxide if it has pet stains. The peroxide usually doesnt affect colorfast cotton dyes and oxidizes the urine out, while also brightening the fiber. I use 35% strength peroxide and dilute it to the 3% rtu. It 11oz. Of water to 1 oz. Peroxide to get to 3% rtu (ready to use).