I, for one, totally disagree with flying with only one instructor.
What if he's taught you something wrong? Or perhaps I should reword - taught you something NOT to the best of your ability, maybe he has a weakness in one particular area.
When I was taught, I had one instructor - we clicked very very well and appeared to have no problems - but every fifth or so flight, I had a "check" flight with another instructor. [It can sometimes be frustrating we all have little differences in the way we teach, but you learn to adapt!]
As for the "no poaching" rule, it goes with what I've written above. What are they afraid of?
I've seen too many instructors hell-bent on getting hours in their logbook and less concerned with actually doing their job properly - teaching YOU to be the best pilot you can be.
Remember DeeCee - you are paying THEM to teach you. It's your hard-earned money - don't you want to put it to the best possible use?
I would ask to fly with another instructor - make it quite clear that it's just for one flight at this point - and then take it from there.
Good luck
Kiwi Chick