I don't really feel comfortable commenting about a subject that I am not that familiar with, but I will do it anyway (as it never stopped me before :-)
Basically there are two opinions regarding what a pilegesh is. Rashi (Beraishit 25:6) holds the only difference between a wife and pilegesh is the fact that a wife has a ketubah whereas a pilegesh does not. Ramban there disagrees and is of the opinion that a pilegesh does not need kiddushin either, she is simply a woman set set aside for him.
According to Rashi, I would assume a pilegesh has all the rules of a wife...as she is considered married in every respect other than the fact that her husband can divorce without financial consequence.
According to the Ramban (and others like the Rambam in Melachim 4:4) things are a little less clear. Ramban writes a pilegesh can simply be sent off at anytime and and her children would not inherit him in any way. (There is more on the subject but for your students that should be enough.)
Also, the prohibition of marrying a second wife without divorcing the first wife is of late origin (only about a thousand years ago and is known as Cheirem D'Rebeinu Gershon) and was not in effect in the times of the Tanach.
Tzvi
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