Dns on VPS versus DNS on HostingCompany


I am having some trouble to understand the reason of the DNS of the VPS box. I put all my DNS entries in the DNS of the hostingcompany as they have multiple DNS boxes and that should be a much safer approach.
However does this mean that I can just can remove all DNS entries in Direct Admin, or will this break things?

One of the issues I am having is that exim sends local inside the box. However we use Google Apps for our mail so all mail should be sent to Gmail.

If I remove all DA DNS entries will this fix the email issues as well? Or should I point the local DNS to the parent DNS at the hosting company?

Any help is truly appreciated!