What is difference between these two examples below, and why?
.1 Alex isn't here. She is visiting her mother.
.2 Alex isn't here. She has gone to visit her mother.
Although the sense of the two sentences is the same, there are subtle differences.
The first tells you two things: 1. that Alex is not present, 2. that she is visiting her mother.
The second also tells you two things: 1. that Alex is not present. 2. that she has left the premises with the intention of visiting her mother.
Whether she is still on the way is not clear. Nor is it certain that she will not change her mind and go elsewhere or have an accident or whatever. All we know is that her plan when she left the premises was to visit her mother.
So the first example puts the emphasis on Alex actually visiting her mother; the second simply lets us know that she has departed with that in mind.