When you choose to "Generate HTML" and choose options under "Open With" that only applies to the first instance of viewing your prototype--you are actually generating the HTML and then opening one of those HTML files in a browser, based on the options you choose.
Axure is simply selecting which of the several HTML files to load. It's default (Sidebar: With Pages Open) is to open the "start.html" file, which is a frameset including the sidebar in the left frame and your page(s) in the right frame.
If you choose "Without Sidebar" then Axure will open a new browser window or tab with your topmost page loaded (probably home.html). That will likely be on your local drive (unless you generated the HTML directly to your web server.)
When you upload your HTML files to your web host, be sure to include the actual HTML page in your URL, e.g., "myWebDomain.com/myPrototype/home.html" and not "start.html" or "index.html" or a directory with no html file, e.g., "myWebDomain.com/myPrototype/ --which most web servers will interpret as "load the index.html file in that directory". It turns out that Axure automatically generates an index.html file which is a duplicate of start.html which means the sidebar will be shown. My guess is that is what's happening in your case, but hard to tell for sure unless you can post a link to your pages.
The good news is you can easily control this. You can click on the little "get links" icon in the sidebar to copy the exact URLs you need for any page after you post your files on your server. It looks like this:
Also, if for any reason you end up with a sidebar, you can get rid of it right away by clicking the "CLOSE" button at the bottom left. Then, have a look at your URL field. That will be the full URL you really want.
Hope this helps! If not, send a quick email to Axure Support (Help > Submit Feedback) --in my experience they have been awesome.