What can be done about a neighbor who claims to own app.1-2ft of land on my side of her wall.
She took down my chain link fence leaving the gate and the remaining fence along my garage wall allowing my small fox terrier to wander the street.
She insists she has the right to prevent me from having a fence bordering the front of the property. I have lived here over 18 months the fence has been there for years. The last 3 months has been hell with her. Now it is getting ridiculous,State of Florida.

You need to check the survey for your property. Make sure where the property lines are. If you find that the fence was totally on your property, then sue her for the cost of a replacement. If, on the other hand, the fence was on her property, then its her fence, not yours.

As for whether you can have a fence or not, that's a matter of local law. Some places do prohibit fences between properties or parts of properties. So you need to check your local zoning rules about that.