Admittedly, I haven't dealt much with setting up virtual domains much but I do believe there are some problems with your initial configuration.
I believe the following lines should look like this (assuming that the fully qualified domain name of your mail server is mail.alexanderweiss.nl):
mydestination = $myhostname,localhost.$mydomain,$mydomain,localhost
myhostname = mail.alexanderweiss.nl
This page -
http://www.postfix.org/basic.html - goes into more specifics about these parameters.
The other curious thing about your configuration is that your mynetworks parameter is set to 127.0.0.0/8. Do you only use webmail and/or do you only permit sasl authenticated smtp? If you want to enable a client machine to send mail through the mail server, then you'll have to include the LAN information in that setting (unless you require sasl all the time).
I don't know if these suggestions will solve your current problem, but they certainly can't hurt to implement. If you're going to edit /etc/postfix/main.cf by hand, then I suggest you make a copy of the current main.cf in case you need to easily roll back should there be issues after editing.
Hope that helps.
-Brian
