There are a couple of options you have here. However, neither is very graceful. If possible, it would be nice if you could change the subVI so that it behaves without requiring events. However, here are a couple of ideas to get you started if you want to leave it as it is.
1. The first example VI I attached, SimulateKeyEvent.vi, is one which I found on NI's website that simulates keyboard events using Windows API calls.
2. The second program is also from their website. It is called programmatic events.vi and may be closer to what you are looking for.
Check these out and see if they get you started. Hopefully, they can give you an idea of what tools are available. Best of luck!
J.R. Allen