Moving or deleting the sym link had no effect at all 
And this works???
certbot renew --dry-run --cert-name chat.icecub.nl
Yup. Works perfectly fine. Returns me new certificate is deployed. Congratulations, all succeeded.
OK, so your homework will be to dissect these two files:
/etc/apache2/sites-available/chat.icecub.nl.vhost
/etc/apache2/sites-available/icecub.nl.vhost
Line by line, char by char, and find out where they differ and why one works and one fails.
And if the naked eye can’t see the difference, manually retype the icecub.nl file over.
There has to be a difference in there… somewhere.
Makes sense. I’ll get right on it. I’ll reply again if I find something or if the issue is solved 
Good luck !
………………
If that happens to fail (at this point I’m thinking it will)…
Also compare:
/etc/letsencrypt/renewal/icecub.nl.conf
with
/etc/letsencrypt/renewal/chat.icecub.nl.conf
That last one finally solved the issue. It turned out that chat.icecub.nl.conf had:
[[webroot_map]]
chat.icecub.nl = /usr/local/ispconfig/interface/acme
While icecub.nl.conf had:
[[webroot_map]]
www.icecub.nl = /var/www/icecub.nl/web
icecub.nl = /var/www/icecub.nl/web
As soon as I changed those to /usr/local/ispconfig/interface/acme instead, the issue was solved straight away and the certs could be renewed just fine.
Excellent !!!
Yup. All certificates are renewed perfectly fine now. Thank you so much for all your help and patience with this! I’m one happy man! 
Glad to help out.
It was hard work even for two of us! - LOL