Just to be sure, the only source of power is at the light fixture?? Huh? Usually, rooms are wired with the line feed coming into the light switch then up to the light. More usually, lights are not on the same circuit as the receptacles. Thus, when you plug in the blow drier the lights do not dim.
So, I'd be happy to develop a wiring diagram . . . but need to know if this is REALLY how your room is setup. For example, can you borrow power from another room for the receptacles, leaving the light on is own from the switch?
Of course, everyone knows you must have GFCI receptacle protection in the bathroom. We can get to that later.
First, can YOU draw a picture of the bathroom, where the power is, and where you want to have things positioned? Your explanation was very good . . . but pictures and 1,000 words .... well, you know.