I have run across a similar situation twice.
For both times (and indeed any instruction I do). I emphasized that when I am instructing I operate the aircraft My way and telling me that Instructor X did it some other way will not change anything and only wastes time.
The first time worked well. Do to time constraints on my part I could not do as much flying as he wanted so he asked me as his principal instructor whether I would let him fly with someone else and, if so could I recommend someone. I ended up hooking him up with another instructor I respected and we coordinated who was going to do what over the course of the training. In the end it worked well and he got done considerably quicker than if he had done all his flying with me.
The other student just told me he had enlisted the services of another instructor, a person I was not very familiar with. It quickly became obvious that that instructor and myself had very different ideas on how to operate and aircraft. I dug my heels in and insisted that my way was the way it was going to be if I was in the aircraft. Not long after he decided to do all his training with the other guy which was fine with me as he had become a PITA and I was going to cease training him anyway.