Remove the little screen and push the button hidden underneath a few times to free it's motion. Should cure the check valve problem. If not it's replaceable.
I've given up on the little rubber cover and have a solid, screw in plug on our fresh water inlet. Solves both problems.
Putting antifreeze in the fresh water tank is a poor procedure. For starters this tank is never completely empty so you're pumping diluted antifreeze into the system and this "tasteless" antifreeze ain't tasteless. Your water will taste "pink" all next season.
-- Chuck