To set-up your homepage to be accessible only through / url you need t:
- Use following key in <appSettings> section of your web.config:
<add key="CMSDefaultPageURL" value="~/" />
This prevents putting .../default.aspx in the url.
- Go to Site Manager -> Settings -> Web site, and set default alias path to your home page alias (e.g. "/Home")
Also on the URLs and SEO, turn off Redirect document aliases to main URL.
Note - this is a slight disadvantage, because you lose the ability to benefit from this setting.
- In CMS Desk, go to Properties -> URLs of your Home document, and set Custom URL path to "/"
That should ensure that any request on the root or /home url will be kept at the root domain path, while still showing content of the home node.