VNC like app.

With Screen Sharing enabled, you can also give it a password for VNC access. When setup like this, most any VNC client should work.

The issue of not being able to bring up a hidden Dock is really a client problem. You have to be able to drag while clicking. For example, the app "Remoter VNC" for iOS needs to use a trackpad emulation to do this. Most of the time, I don't bother switching from the normal tap-click interface and just use Spotlight to open an app. Switching between apps with CMD-TAB works well.