The links in an html property are re-evaluated each time it is rendered, so it should pick up any changes you make to the address of the destination page. I just tested in the basic demo site upgraded to the latest Webnodes version.
When you add the link in the editor, the link is in the format of "/basicdemo/about-us".
When you save that node, it is replaced with a url like this: "/basicdemo/?nid=135".
When you render that page, the link is re-evaluated, uses the friendly address of the node being linked to. If you change the node being linked to, the link should be changed as well, the next time it is rendered.
In my tests it all works as expected, in both Chrome and IE. I'm not able to reproduce that it changes to "Local specialized address".
If it still doesn't work as expected for you, try to upgrade to the latest version of Webnodes if that helps.