Thanks for all your answers.
I've implemented both sites on 1 ip address now where only the first domain has an ssl certificate. Both are accesible through http. On the internal network all is ok.The strange thing that happens now is that when I access the first site externally with https://.
... I get the second site in my browser. Turn me upsite down, but where have I gone wrong... Or does namebased virtual hosting not work externally here because of your earlier pointers. Please keep in mind that if you look up the word "expert" you won't find my picture as part of the explanation.....;-).