What I'm hearing in the history of the issue here is a story that is likely to have two sides to it. If you had explicit examples of your immediate supervisor behaving in a clearly unprofessional manner, then I would endorse taking it to the boss' boss immediately.
But I'm hearing the type of issues that are very closely correlated to point of view, for example:
"Type Cast" - people get asked to do the roles that their bosses see as appropriate for their skill levels. Could the boss see more in you? Maybe. But some of casting people into roles is overall making use of the entire workforce as efficiently as possible. So if there's a person out there with better skills than you, you may be stuck in the role you are in. It'd be great if everyone always got growth opportunities, but that's not always possible.
"finding fault in trivial things" - trivial is a judgement call. You may see it as a small thing, he may see it as a big thing. But particularly in management, small behaviors and details can make a BIG difference in the health and morale of a team. And reference previous point - if you score a 9 out of 10 on the Awesome Manager Scale, and the other guy in line for the role scores a 9.5 - then it's true - the things you need to do to make the cut are trivial, but they are nonetheless important.
"Making progress" - it's a great sign that the manager is actually acknowledging your work. But sometimes it's not just changing behaviors over a short time. Making a push to change habits is great, but often it won't stick become a default behavior until you've been at it for a while.
So, I don't think you can reasonably expect to walk into the bigger boss' office with a list of complaints and expect gratification. It may very well be that your boss and his boss have already talked about this role, and how they'd like to staff the work in the company.
My thought would be - overall, keep it positive. It's fine to say that you are:
- Really eager to move forward into larger management roles
- Keen to improve any gaps in your skills
- Actively taking the advice your manager gives you - you can even mention a few of the areas you're working on
It's even OK to ask your boss' boss if he has any additional thoughts in what he'd like to see in more senior managers. But realize that the bigger boss has delegated your development to your actual boss. If steps in the middle of that relationship, he could very well be undermining your boss' authority, and that's not something a good senior manager will do lightly.
The one thing to avoid would be any form of ranting - keep any discussion focused on ideas for generating positive results rather than simply focusing on the problems at hand. It's actually amazing how many things can be expressed this way... for example, if what the boss is asking for is really trivial - like sorting paper clips by color or something - you can say to the big boss - "I'm doing my absolute best to be a better manager - for example, I've been sorting paper clips by color, just like my manager has asked." - any boss in his right mind will realize this is a mind-numbing exercise and will likely step in to a put a halt to sorting paper clips by color - but he's able to do so at his own discretion without having to listen to you rant and without getting a poor impression of your attitude.