What is the term for two mutually exclusive, contrasting emotions
In terms of systematic desensitization, you're thinking of reciprocal inhibition (see, e.g., Wolpe, 1954).

For what it's worth, beyond this literature, there's a general debate about whether positive and negative affect can be experienced simultaneously.  (Indeed, Emotion Review just published a series of articles about this.)  It's fair to say that the debate has not been resolved.