an advice column for Pilates Teachers

I have had a duet in my schedule for 5 years.  They come faithfully 3 times a week during peak time-slots.  We have a lot of fun in our sessions and have created a great relationship.  However about 2 months ago, something went sour between the two of them.  One is getting divorced and has accused the other of divulging information shared during Pilates to another person.  The accused maintains she did not and in fact it was the soon-to-be ex husband who shared the information.  Both are digging their heels in that they are right and it has made the sessions so uncomfortable.  What should I do here?  Should I try to broker peace?  Should I offer another time slot so they can separate?  Should I just stay quiet in the weirdness?" ~ Stuck in the middle