Karen,
I read this post for the first time today and noticed that you have not responded. I hope you found your fix and would be interested to know how it worked out.
When you hook up to city water it has nothing to do with your gray tank. They are completely separate systems. It sounds like to me that you have a leak in your fresh water system somewhere. If water is leaking out from under the trailer "by" the gray tank, it most likely is a sign of a leak above the gray tank. If not properly winterized in the fall pipes can and do break and that is what you are probably faced with.
One way to tell has already been proposed. Fill the FW tank, disconnect the city water and turn on the pump inside the trailer. If anything is leaking you will find out quickly.
Let us know how this works out.
