My first advisor wants me to include my second advisor's name in a paper that I worked on before she (2nd advisor) came along.
Should I include her name even though she didn't do anything in that paper? I don't think she even read it.
The behaviour of adding non-contributing authors is not considered good practise; quite the opposite. The Vancouver protocol specifies what is needed to be included as (co-)author. See descriptions at ICMJE and BMJ.
The basic points are as follows:
Note the "AND".
There are also several posts on the tag authorship here on Academia that can be of use.
For someone to stand up against one's advisers is of course difficult and it is easy to state that one must do so. It is necessary to assess the situation and read up on the recommendations provided by learned societies such as BMJ and use that as part of your case. I strongly recommend this paper for students from APA Science Student Council.