Is three citations per paragraph excessive for undergraduate research paper?
If you are asking whether it is a general "best practice" for a research paper at any level to have three citations per paragraph: no, it is not.  In any level research paper, you should cite as often (equivalently, as little) as necessary in order to inform the reader of relevant prior work.  If seven papers are relevant to what you are saying in a given sentence, you should cite those seven papers.  If in a paragraph you are not saying anything that makes reference to or would be aided by making reference to prior literature, then there should be no citations in the paragraph.  You never insert citations to meet numerical requirements.

However, this is an assignment for a course, so the best practice is whatever your instructor told you.


  The way that she phrased it left uncertainty whether this was for every paragraph, or only for the quoted ones, so the context of whether similar works have this level of quotation in them is the only standard I have to go by.


No, you can ask your instructor which of the above is what she wants.  I encourage you to do so.