I can't help but think that Umbridge's circumstances might actually be somewhat similar to Parkinson's; a not particularly clever woman who attached herself to someone that can help her make sense of the world. It's just that Umbridge is very visibly unpleasant, while IIRC Parkinson is pretty much a non-entity in the books.
Also, Umbridge just bit of way more than she can chew. Sure, she might inconvenience Doug and Dumbledore, but while Dumbles isn't likely to commit murder or even anything worse than sheer abject political humiliation, Umbridge's shenanigans in canon (never mind here in this story) are sufficiently dangerous that Doug might just lay down the hurt on her if she pushes in the wrong way, and not just physically. Doug is more than capable of finding out every faultline in her mind and exploiting them until her utter ruin.
Also, Umbridge just bit of way more than she can chew. Sure, she might inconvenience Doug and Dumbledore, but while Dumbles isn't likely to commit murder or even anything worse than sheer abject political humiliation, Umbridge's shenanigans in canon (never mind here in this story) are sufficiently dangerous that Doug might just lay down the hurt on her if she pushes in the wrong way, and not just physically. Doug is more than capable of finding out every faultline in her mind and exploiting them until her utter ruin.