We use Digital Ocean, which provides high speed internal networking in additional external networking. The internal network uses 10.136.0.0/16.
Unfortunately, Digital Ocean does not provide split horizon DNS. We'd like to stand up our own DNS server to respond with the internal addresses when an internal server resolves another internal server and they both can talk over the 10.136.0.0/16 network. We do not want our DNS server to be a single point of failure though, so we want to keep Digital Ocean's DNS servers in the configuration, but at a lower priority.
Is there a way to specify a priority of DNS Servers? For instance, for our domain www.example.com, could we direct those queries to our internal DNS first before trying Digital Ocean's DNS?