Being an old timer here, i am lie Jim R on this. If I was your instructor, i would not be upset that you went to train with your old instructor. But, I would be very P***** that you did not come to me and ask me first. It would make me question your honesty. If you would conceal or lie about what seems to some people to be minor, I'd wonder just how much I could trust you. In my early days of training, I asked my Sensei if I could also train at another Dojo on nights when we did not have classes. He told me in no uncertain terms, you can train here, or you can train there, but not both. Make your decision. I stayed in his class.
I think you should discuss this with your current instructor and be open and honest. your friendship with your old instructor does not release you from the responsibility of what is right. Remember it was you who changed to the new school. You need to be up front with your current instructor. that is the right thing to do. If you train with someone, you should be ready to abide by their rules.
I run into students all the time that have the "I am a customer, so I can choose what I want to do". what they, and possibly you, fail to realize is that your instructor is not charging you what he is worth. When a student threw that comment in my face, I quickly told him that I had put decades of my time, money, and blood into what I freely decided to share with him. There is no way that he could possibly pay me what my experience is really worth. The fees that students pay in no way cover the cost of what i offer them. So it is with any good instructor. I'm an easy going guy. i teach in a relaxed mode. My students can call me by my title, by Sensei, or anything respectable. I'm not demanding. but I will not put up with anyone that has the I pay for training so I'm the one that decides what is OK for me to do. Understand that I encourage my students to go to other schools and work out, or observe. it only proves to them that I can teach them as well or better.
...