That's a typical problem for C level. The CTO or even the CEO will have to deal with it, as that's exactly their function in the company: taking decisions about operations. Neither a stakeholder nor a VP has this power, so if they don't want the other stakeholders to fire them because the delays in projects cripple the company, they better address the problem.
Your role in the matter is simply to let them know what's happening, and let them do their very job.
And if they decide to let the VP do her thing, then there is nothing more **you** will be able to do!
Don't forget: your hierarchy is fixing your priorities, not this person. If you are stuck between your hierarchy's order and the VP's order, refer to the hierarchy and let them decide what to do. If the VP is unhappy with that, just say her to check it with the C level, as you are not allowed to change your priorities.