Re: Two teachers...
I didn't tell my sensei the first time I trained at another dojo (during a couple of weeks when mine was closed). I got chewed out over this by my friends, it set up weird political undercurrents with the other sensei, and it made me feel sneaky and guilty--all in all, a bad decision. The next time I told her, she gave her approval, and that was that.
I currently train a couple of times a month at an Aikikai dojo, paying mat fees--usually I'm there for their open mat night, but occasionally for an actual class. They know that I am not their committed student, but they also know that they offer something I really value--a much broader training in ukemi than my home dojo--and apparently that's okay with them.
I try to do what I'm shown in each dojo, but the Aikikai folks can glance at me and see that I'm not one of theirs--"oh, *that's* why you're so light on your feet," as someone who had just trained with me for the first time said recently. If this bugged them I would leave, but so far it hasn't. I strictly avoid talking about one style when studying the other, except when questioned directly--that can get awkward really fast.
So far this has not caused me trouble at home, though it could--I have been taught a few techniques that my sensei regards as unsafe, and mustn't do them in randori. I'm sure that if I had tried to keep the cross-training secret I would have been caught out long ago. The Aikikai school blocks atemi that the Ki Society school would dodge, and I blocked one from a junior instructor the other night. He just grinned and said "Beats getting hit."
I am in favor of training at multiple schools if the student wants to do it, but I would strongly recommend being honest with both teachers and keeping an eye out for potential problems.