You can install a 3/4" garden hose shut-off valve (mine has this)
That is what I did, with a Y connecter. There are two advantages to this. It is really easy to turn off the water when I leave the trailer and when leaving the RV site I can release the pressure through the unused Y connection.
The check valve is an internal part of the city water assembly. You can replace the city water assembly You can plug it off with a 3/4" PVC plug You can install a 3/4" garden hose shut-off valve (mine has this)
There is a check valve in the city water connection that is known to fail. It can be replaced and some report fixing it. As I understand it, there is an O ring that becomes displaced, often by someone relieving pressure by pushing on the valve.
The easiest thing to do is buy a cap for the connection at the hardware store.
It seems your one way valve at the city connection is either stuck, or broken. You could try lightly tapping on it, to see if it pops back, or it may need replacing.