Moving website from one provider or web partner to another is not a big deal as long as you have control of your domain name. Everybody should have this control over their domain name, do not leave it to your web partner. With this control you decide what will be seen by someone browsing to that domain. Even if you fall out with your current web provider, you can create a new site and even do URL or 301 redirects to keep the history that you created with the old website. This history is very important and these redirects are essential. Any new web partner should include these 301s in any quote. Watch this short video from Googles Matt Cutts to see what we mean.
http://support.google.com/webmasters/bin/answer.py?hl=en&answer=83105