Sympathies, it sounds like a difficult situation. I can emphathise as I lead a quite tricky and technical speciality within a department/group which is a bit of a hotch-potch of very different areas and types of work, some require much more specialist knowledge and qualfications than others. Realistically no manager/director is going to be an expert in all and nor do they need to be (and I am always going to be the only person with expertise in my own area, that the fact is what keeps me employed in the grade/position I have at the end of the day, if my managers had the know-how I do there'd be no need for me, or not someone at my level anyway), I myself know next to nothing about some of my peer Heads of Departments' work areas. It can be quite a lonely place to be, as like you over the years sometimes my managers have been very disengaged from my speciality and don't turn up to meetings etc. and don't seem bothered about what we do, at other times (usually when there's been some kind of crisis) they steam in and interfere with what they don't really understand and mess things up or make silly requests or suggestions that I then have to soothe over with my team. I totally get the patronising emails explaining what you already know etc. which can be quite infuriating.
I do think however it's pretty much just a normal part of 'managing up' and to some extent you do as a professional and senior manager just have to get over your annoyances, and accept that you are the bridge for your team and have to try and present senior management to them in the best light, filtering out and translating to your team what's been said to you in words they'll understand, as well as vice versa. I sometimes imagine myself being a sort of ambassador/diplomat from planet 'senior management', as far as my team are concerned they might as well be aliens so little do they understand what they're on about.
I do definitely think you need to get over your annoyance that she's had success at a young age without having much technical/speciality knowledge or experience, there is a skill and an art to management/leadership as a thing in itself, it might not be one that you value that much or think should command the salary it does but that's not your decision to make. And if she really is incompetent and promoted beyond her capability that will likely have it's own consequences, these things tend to work themselves out in the wash eventually. And of course if you want to leave, leave. Generally I find once you start feeling undervalued like this your best course of action is to accept this job's given you it can and it's time to find somewhere else rather than painstakingly screwing value out of the dregs of a role you may just have outgrown.
In the meantime though, why exactly are your team feeling disengaged, is it just a case of she hasn't met them whereas she has the others so they feel a bit 'lesser' or unloved? If so that's pretty easily solved and doesn't need to be made into a huge deal with accusations of favouritisim or incompetence, I'd just have a casual chat with her and say 'X would you like to come along and observe part of our team meeting on Y date, perhaps you could say a few works about departmental priorities, I'm sure the team would love to hear from you' or similar? She's probably feeling a bit anxious that your team are going to throw loads of technical questions or issues she doesn't have the answers to at her so if you can reassure her that's not the agenda or that you will answer/shut down those types of things that will be better.
If there are more fundamental problems you need her to be aware of I would just get a bit pushy about putting time in her diary to meet, and if she keeps cancelling email her - I'd try and frame it as 'here's X problem, my solution is Y, let me know what you think' though rather than dumping a load of issues at her.
Hope that helps!