MacBook Bound to Active Directory Domain
My Macbook is also bound to a AD domain, but I do not have any such DNS issues. DNS settings are configurable per network connection type in System Preferences. System Preferences>Network>Advanced>DNS.

Simply edit (if allowed?) the DNS entry for the connection type. You can have more than two DNS entries, so for example, you might simply ADD Google DNS to the work DNS. In this case, if the work DNS are not available, it will fail-over to Google DNS.

You could do this for all network types, or perhaps just for wifi, if you use a hardline at work.