One reason that could explain why you are not able to edit your tree right could stem from the difference between the types of trees that you could have online.
There are three different types of trees that you can have on a family site; a Web Tree that was made online, a tree that was imported to your family site using a GEDCOM file, or a tree that was made in Family Tree Builder, and published to your family site.
When you create a family tree in Family Tree Builder and publish it to your family site, you CANNOT edit the tree online. If you built your tree in Family Tree Builder, each time you would like to make changes to your tree online, edit your tree in Family Tree Builder and then re-publish your family tree to your family site. This will update the previously published tree (with the same name) on your site.