Controlling the RTS is pretty simple. You can do it with a VISA property node. Select Properties>Serial Settings>Modem Line Settings>Line RTS State. Change to property to write. Valid inputs for the property are Asserted, Unasserted, and Unknown. The input is an enum and you simply have to right click on the property and select Create>Constant.
The big problem you are going to have is timing. If you are working on windows, timing is not even close to being deterministic and getting accurate and repeatable pulses is not possible with software timing. You should look at using something hardware timed. Some of the NI DAQ boards have a counter output that you can use.