I faced the same problem in my website. As you mentioned in your question :
Usually, the Pathauto module doesn't allow to the users to create the node with existing URL by giving the error as "Path already in use"
This is true only when you hand code the URL alias. If "Generate automatic URL alias" box is checked then similar URL's are appended with numbers at the end (like in your case).
The method I used to solve this problem was to install a module called Unique field which makes sure the no 2 nodes have the same title(and thus unique URL for each node).
Suggestion :
This is just a suggestion for URL structure and SEO. A general rule of thumb that I follow when creating URL, is to rank the keywords in the URL. The highest ranked keyword should come at the end of the url. For example www.example.com/less-specific-keyword/more-specific-keyword. This way you can rank higher in search engines for the same content and also users can get an idea about your content just by looking at the url. For example, in your site you can structure the URL like this www.example.com/state/park/park-name.