Yeah the load balancer was just intended for the application servers. Running a hot DB secondary with just read accesses is possible by setting up manually, but tends to require a lot of maintenance work during updates in our experience.
To be honest, we have not figured out how to connect the DO servers to AWS yet. Do you have experience with that?
Having a cross-datacenter VPN is one way. But I am not sure about how bad your latencies will end up. Most likely they won't be performant especially in the case of an ACID compliant DB.
To be honest, we have not figured out how to connect the DO servers to AWS yet. Do you have experience with that?