Re: Two teachers...
I do not think you have to ask, Christopher.
But you should tell both instructors.
Later I wouldn't mention the dojo. Definitely I would not encourage you to say "... but in xyz we are doing it that way.
And for yourself you should define your primary dojo, i.e. where you want to promote, etc.
My sensei knows that I randomly visit other dojo, but I do not tell every visit.