Dear Lisa,
Yes, your son might display Separation Anxiety Disorder, but that alone would not account for his anger and oppositionality (in fact, most children with Separation Anxiety alone are more on the quiet/worried end of the spectrum).
The difficult behavior can be the result of developmental immaturity and his not really being ready for the kinds of social interactions he's encountering. The behavior can also indicate an emerging Mood Disorder, though this is very difficult to diagnose in a child so young. If there is any family history of Mood Disorder (depression, bipolar illness, e.g.), it would significantly increase the probability.
It wouldn't hurt to make an appointment with a child mental health professional to help you sort out what is occurring, and to help you develop a plan to respond to your son.
I work with a individual that has these rapid mood swings and also a cousin with the same mood swings, my friend is diagnosed manic depressive and my cousin is diagnosed with bipolar personality. You might try looking into the bipolar disorder as a possible explanation as to what your son is experiencing.