For me, the key to all this is to concentrate on the main verb, "persuade". We all seem to agree that "he" is the subject and "persuade" is the main verb.
"Persuade", whether viewed as a transitive or causative verb has be used "on" someone (or something, like a dog) in the form of persuasion.
Therefore, whether viewed as a transitive, or causative verb, the action has to have a direct object that receives that action. She would have gone if
he had not persuaded
her otherwise.
If we agree that only someone or something can be persuaded, then the only someone in that sentence other than "he", which we have already established is the subject,
is "her" which must therefore be the direct object receiving the persuasion.
He cannot persuade "not to go", because firstly that does not make sense, and secondly "not to go" is a phrase (however, we care to view it), and not a person or animal.
It therefore cannot receive his persuasion.
This means that the only possible direct object in that sentence has to be "her", otherwise you end up with an illogical mess in my opinion.
So I think the key place to start in this instance is logical meaning first, then grammatical analysis second, and if the two agree then we have found the answer.
(But I still bet we haven't reached agreement. I've probably just rattled the hornet's net with a big stick! :lol
.