. The issues is getting the hospital to grant my home server permission to be accessed from within the hospital environment. The hospital will not allow me to move the physical server into the new office. I would have to "virtualize" my server in their environment and then won't allow me or my IT person access to it independently.
That sounds like the best option. You will have admin access to your virtual machine but not the Hypervisor. That's exactly how services like Azure work. You don't need access to the Hypervisor to administer your virtual machine. Makes life a lot easier because they're responsible for maintaining the hardware.
Other cases like this we've setup entirely separate networks. Just a simple access point for a WiFi network with a server onsite which is a completely separate network. There's many ways to make it work with the hospital restrictions.