It doesn't seem like it changes the meaning in an obvious way. Does the order of adjectives matter or is it just in my head and just due to happening to phrase it one way rather than another more often?
Main is a comparative adjective used to compare between objects.
If you have several external sites, one of which is more important than the others, then that site is your main external site. You may, or may not, also have some internal sites, some of which may be more important than your main external one.
If, out of all your sites, internal or external, you have a most important one, then that is your main site. If this site is external then you can describe it as an external main site, or more commonly you would say that you have an external main site. Your most important site is external.
It is like having a French best friend, this means that your best friend is French. If you say you have a best French friend then he or she is the best out of all your French friends, but you may have better friends in England or Germany, for example.