since the content added to an html editor instance needs to display correctly on any page of your site, the image path needs to be relative to the server root.
for this to work from a testing server to a live server, you need to set the testing server up using the same site relative path.
one way to accomplish this is to use a subdomain for the testing server:
test.mydomain.com/
this way the same site relative path that works on the subdomain will work on the live domain.