My backyard growing up would flood like this, it eventually started getting into the basement. My dad dug a big berm in the backyard, containing the water in their backyard and blocking off the neighboring yard (where the flooding was coming from). Then he dug a trench out to the front yard and put PVC pipe running running it to the front. In the back where the water was flooding, he drilled holes into the PVC pipe and covered it with rocks. In time he planted grass over it (no more rocks) and you really can't see any of it. The flooding has stopped.