I also free range mine from 8:30am-5:15pm(this is when I set the auto opener)
I keep my feed strictly inside the coop. I have them on about 5 acres and I like the fact that they have to come back to the coop for food and water. (Keeps them from wandering too far) It also keeps the food dry when we have unexpected rain showers.
I also have 2 donkeys and a horse in the pasture with them, and they unfortunately have gotten a taste for chicken feed so my reasons are probably different from yours.
With 2 coops your in a different situation than I am, and as long as you have food and water in both I don't see a need to drag the food outside. (That's just more work for you) The water is a different story, it won't matter if it rains, so go for it.
With the feed I would be concerned that they would spill it and then the feed on the ground left outside is both an attractant to other animals after dark, and possibly after a rain is going to mold and be useless anyway.
Just my 2 cents anyway!!