Marion, applauding in the middle of a tune to show extra appreciation is common in some contexts -- jazz performances, for instance, where the musicians take turns soloing. It's the audience's prerogative, and it can give the performers a boost if taken in the proper spirit, so I wouldn't be inclined to stifle it.

If you find applause distracting, the solution is not to try to stifle the applause -- the solution is to learn to accept the tribute without losing your focus. It's a performance skill, just like all the others (sequencing your material, making smooth transitions from one song to the next, speaking to the audience, tuning on the fly, etc.). The more you do it, the better you will get at it.