Is there a reason you don't have the two instances pointed at the same database?

If you have two instances, you can point them at a shared database, and they would have all the same processes and such so you don't have to manage it in two places.

You just disable the routing service on the secondary one (i.e., the DMZ instance), then you can very easily have the kind of process you want.

For example, we have two servers, one internal and one in the DMZ, the DMZ instance has our public portal license for public forms. The routing server and automatic windows login are disabled on the public instance (there's a separate STS site on the DMZ one).

As a result, there is only one database, and the internal routing service handles the workload, so the public site is really just there to do the data capture on public forms.

Another bonus is that employees can log into the public Forms site to fill out internal HR forms and stuff like that without having to use VPN or be physically present in the office.

If they are completely separated, then the only way to do what you want is to have a process created on both servers and use WF or something to initiate the process on the internal Forms instance after submission.

You can export/import process profiles, but you can't export just the forms, so once you've made the customizations to the business process model specific to each forms server, you would need to manually copy any changes to the forms.

This could become very tedious, especially if you start getting more public forms, so I think you'd be a lot better off looking into the shared database approach.