The way it is written is correct and your suggestion is also correct, but they don't mean the same thing. "to relax ones mind" is not a physical relaxation and it means that it can be assumed that the person's thoughts were at one point more chaotic, but now the person is mentally relaxed and calm. "to relax" in general, refers to a physical response. So if you simply say "she relaxed a little" it may not be clear whether the relaxation response was a mental or physical one.

It is fine. What is better to write depends on who is writing it, and what they want to convey.