If they are asking you to report upwards, bypassing your manager, and they are not actually doing anything to address these issues with her directly, then they are behaving very unethically if you ask me! Tolerating crap management is not "nice", it is just negligent - and crap management on behalf of your line manager's line manager, I think!
Senior managers should not be undermining her by discussing her weaknesses with the staff she line manages, but addressing the issues with her so that she can do something about them. If she is able to improve, then she should be given training, support and guidance to do so. If she isn't able to improve, then she shouldn't be doing the job. and they need to manage her out of it.
I have worked with a few managers who have been promoted beyond their capability, and like you, I have been asked on several occasions to inform on them to more senior management. I have always operated on the policy that I wouldn't say anything to the higher level managers about my boss that I hadn't already said directly to his/her face. At least then, my own conscience has been clear.
Bear in mind that it is incredibly stressful for someone to be in a role which is beyond their capability, and your line manager may well be torturing herself with this knowledge already. One former boss of mine committed suicide as a result of this situation, and it was horribly distressing for all concerned. I think it's fine to share your concerns with senior management, but if you want to act with integrity in this situation, I think you owe it to your manager to have an open and transparent conversation with her first, expressing your concerns as sensitively and as diplomatically as you can.
If you spell out what communication and support you need from her, and she still doesn't respond, then I think it's reasonable to take your concerns further up the hierarchy. But at least you should give her a chance, and you might actually be able to help her by getting her to recognise where she is going wrong.