In this case I don't have full access to it. (hostgator) Can I install/use a svn repository for my code ? I'd like to kill two birds with one stone since I already run a website off of it.
Short answer is no..
I would look at outsourcing it to store your repo in another location then your website. 1 disaster you lose the site and your repo.. Not a good idea
Visual SVN Server should allow so.
Please see some features here: VISUALSVN SERVER // Features.
During the repositories creation, you should be able to specify the URL somewhere in the configuration. The full URL might demand the Repository name in it, though. That is more likely what you want, if you don't want any user to come to your repository source control page whenever one type your URL.
However, I guess you will have to use this same server for your repository. What I mean is that you will have to install Visual SVN Server on this Internet-exposed server.
I just can't say whether it is possible to install it on the LAN-side of your network, and expose your repositories through your website URL. This might be doable too, and would benefit of a greater security, I guess. Visual SVN allows for HTTPS connections. This might be sufficient.
Such configuration might get risky over time if your webserver gets hacked or whatever, and you lose your repository...
Sorry! I assumed you had your own webserver infrastructure home/office. With such hosting, I wouldn't recommend doing so, but this might be doable. Take for instance SourceForge which offers different source control URLs for different open source projects.