That's right. When a pronoun is a simple object, it takes accusative case, not nominative. No one would ever say *"please let I in" rather than "please let me in".
However, in this example the object is not she, but she [ who would rend this family because of her own agenda ]. That is, the object isn't just modified by a relative clause, it actually contains that relative clause. So, our usual rule doesn't necessarily apply.
And here, the gap left in the relative clause is in subject position. That means the relative clause wants to assign nominative case, while the matrix clause wants to assign accusative. That's a conflict, and it needs to be resolved somehow. Perhaps a speaker might resolve this conflict two different ways, picking either her or she:
How I despised [ she [ who ___ would rend this family because of her own agenda. ] ]
How I despised [ her [ who ___ would rend this family because of her own agenda. ] ]
The first takes the case from the inner clause, and the second takes the case from the matrix clause.
Which is correct? Well, the easy answer is to say that the inner clause assigns case, so she is correct. And certainly, I think many speakers would agree that she sounds better. But many speakers prefer she even when the gap in the relative clause is in object position:
I saw my wife and children, my dear cousin Diomache, [ she [ whom I loved ___ ] ] .
(From Gates of fire: an epic novel of the Battle of Thermopylae, via COCA)
And of course the gap may be in neither subject nor object position:
[ She [ whom a man can not live without ___ ] ] has become a goddess . . . .
(From Feminists, Meet Mr. Darwin, via COCA)
Here, only the matrix clause assigns nominative case, and yet our earlier rule was that the inner clause assigns case. But would any speaker accept this example with her? I'm not sure, but I wouldn't. At this point, we have to abandon our earlier rule; we could try a more complicated rule, such as "the inner clause assigns case in objects, while the matrix clause assigns case in subjects". It's a better rule, but clearly it's not 100% accurate. In fact, we'll struggle to come up with a rule that explains modern usage in terms of case.
I think what we see here is part of the long-term trend away from the case system in English. I, like many speakers, prefer she in examples like these, regardless of whether it's assigned nominative or accusative case by either clause. And consider examples like the following:
[ She [ whom thine eye shall like ___ ] ], thy heart shall have ___
(From Doctor Faustus line 594, via The Distribution of Pronoun Case Forms in English by Heidi Quinn (p.307))
Nothing in this sentence assigns nominative case, and yet, here it is: she, not her! Of course, this isn't quite the same English we speak today, which you can tell by the presence of thy/thine and the choice of thine before a vowel, but it does illustrate the trend--my modern ear agrees that she is better in this sentence than her.
For some speakers, formality may be a factor. When she or her are used as predicative complements rather than subjects or objects, both forms are acceptable: she is more formal, while her is less formal. Compare the following:
It was she who said it. (formal)
It was her who said it. (informal)
And we may see a similar effect here by association. Speakers who would normally use (or at least accept) her in objects containing relative clauses might instead prefer she in your particular example because of the relatively formal wording.
My personal preference is for she in your example, but her sounds okay to me, too. Why? I don't know, and I can't tell you for sure why other speakers make the judgments they do. But If I were forced to come up with a reason for my own preference, I'd say it's because she who sounds better to my ear than her who. For me personally, it's not a matter of formality.
But regardless of the reason, as far as I can tell it's standard to use she in sentences like yours. The author has not made a mistake.