No direction from my director and boss

My boss, a franchisee of a quick service restaurant chain, hire a new director 7 months ago to help with a restruturing process of his company. He owns 22 stores in 3 different areas. I'm one of 4 supervisors who each have 5 to 8 store's managers to direct. Each store have 10 to 16 employees. None of us have training nor courses in management. I've been working in that company for the last 14 years and have seen it going from 6 stores to 22.

My problems are :

1) The new director doen't have a clue about managing and restructuring. She doesn't know anything about the operations of our restaurant chain and and often says she's too fancy to eat in our restaurants. SHe's very insecure, she micromanage each supervisor (except me because I've too much experience for her) and she's getting really upset when they do anything without first getting her permission. She upset everybody she works with (many people left the company) and always try to make her more important and competent than anybody else. She neglect to give direction and act on little unimportant things. She haven't talk to me within the past three months. I've received 3 e-mails from her during those months : one to ask to look if on of my stores need a new openig hours sign, one to ask if all stores have the right pipe's colour for the washing soap, and the other also for and not so important thing.

2) My boss just start to be a little engaged in the management of the company. I've been by my own trying to give a direction to the managers during all those years. No training, no performance review about my work. He doesn't seems to really know where to start to restructure the company. He can see his new director doesn't do the job, but seems unwilling to do something about that.

As I listen to MT podcasts since more than a year now, I have a pretty good idea as where to start to help the company. I present that to my boss and he was open to the ideas, but he wants our director to take the lead. We present that to her, but she still focus on unimportant things. She just didn't get it. She started to read books about "how to lead", but doesn't act on her leadership.

I'm now wondering if I should left the company to be able to go further in my career, but I'm afraid to do so because I haven't any official training in management. Also I don't know where to look for a new job as there's not many restaurant chains that have franchisees that own many stores like my boss. I'd like to hear about your thoughts about my situation.

Marie-Claude