Apache: configure prefork in a per-virtualhost way

That's not how it works. A virtual host is based on either IP address or on hostname, not on path. But there are a few other things you can do to achieve the same objective:

• If the server1 virtualhost has a separate hostname, you could have a redirect
• If all you want is to serve content from a different path for that URL, you can use an AliasMatch to map that path
• You could use mod_rewrite to do an URL rewrite according to your specification

I can't be more specific than that without knowing more about what exactly you want to achieve. But I believe the Apache documentation on mapping URLs to file system will give you a good starting point.

When I lookup your domains, I get 2 different IP addresses. In this case your configuration needs to be something like this:

# This is the "main" server running on IP_ADDRESS_OF_DOMAIN_tsk-run.tk
ServerAdmin webmaster@tsk-run.tk
ServerName tsk-run.tk
ServerAlias www.tsk-run.tk
DocumentRoot /var/www/html/tsk-run/public_html
ErrorLog ${APACHE_LOG_DIR}/error.log
CustomLog ${APACHE_LOG_DIR}/access.log combined

<VirtualHost IP_ADDRESS_OF_DOMAIN_tsk-test.tk>
    ServerAdmin webmaster@tsk-test.tk
    ServerName tsk-test.tk
    ServerAlias www.tsk-test.tk
    DocumentRoot /var/www/html/tsk-test/public_html

    ErrorLog ${APACHE_LOG_DIR}/error.log
    CustomLog ${APACHE_LOG_DIR}/access.log combined
</VirtualHost>

Replace IP_ADDRESS_OF_DOMAIN_tsk-test.tk with the IP address of this domain.

See apache documentation section Name-based hosts on more than one IP address for more details.