I have this strange ability to be able to control the events and environment in my dream. I know the term lucid dreaming means that you are aware of being in a dream, but this goes a step further. Is there a phrase to describe this kind of dreams?
The most common phrase seems to be dream control (Google, Google Books). I think this is also the most likely to be understood: it means more or less what it sounds like it means, so even people who haven't encountered it before will probably have no difficulty with it.
(I found dream control by skimming through the Wikipedia article on lucid dreaming; and I found dream programming by skimming the Google Books results for dream control and seeing that one of the books mentioned it as a synonym; and I found dream incubation similarly from the results for dream programming.)
This is more a question about scientific terminology than the English language in general. However, the term you are looking for is simply Lucid Dreaming. In sleep studies, this is the term used when a subject is able to control the dream.
The stage when the subject is aware that they are in a dream but are unable to control it is known as Pre-Lucid Dreaming.
There are several references to this that you can find with your favourite search engine. There seems to be no agreement as to when one state changes to the other. I have seen references to degrees of lucidity, attempting to create a scale of control of the dream. Also the use of other prefixes such as semi-lucid, quasi-lucid etc. All these qualified forms relate to a lack of control, leaving Lucid Dreaming as the term for being in control.
Your best bet is probably to define the term when you use it, so as to make it clear to the reader.