If both DNS servers are configured to be reachable, and have different records, you are breaking one of the fundamental precepts of DNS, in that all records must match - the reason this precept exists is because if one DNS server is busy, the secondary DNS server responds with the answer. Thus, if the records differ, results will be different, which is what you are seeing. What you'd need to setup is an internal DNS that servers the internal IPs of the site and point your clients to that DNS array ONLY, and then setup an external DNS array that serves the internet facing IPs that internet DNS servers will query for lookups.