Rewrite url from subfolder to another domain

I′m sorry if the topic is misleading. Hopefully you will understand what I am going for.

I have installed WordPress in a subfolder in my public html-folder on my server, where I have another WordPress installation in the root folder.

I have directed my domain to the subfolder by specifying the nameservers of my server at my domain provider. Then I have added an Addon domain in Cpanel on my server that points to the subfolder – where my WordPress installation is.

This makes me able to surf to familjenviderot.se and land in my subfolder at my server. But all other pages on the site gets the url hemskankt.se/familjenviderot.

Is it possible to have the whole site to have the url familjenviderot.se

So instead of hemskankt.se/familjenviderot/about I would like to have familjenviderot.se/about