A rider may only have one dragon at a time and a dragon may only have one rider at a time.

In the case of Dany she can only ride Drogon. If you look more closely at Viserion and Rhaegal she can't properly control them. This is evident in the scene on the cliff side when they are climbing around her and they snap at her.

The reason she has some form of control over them is that she is their mother and so has a bond with them. This bond is not strong enough to form a close enough attachment to be the rider though.