、。
It looks like she'll refuse to follow his advice — she dislikes him, after all.
Literal
She [topic-は] his [genitive-の] advice [to-に] follow act [object-を] looks-likely-to-refuse, that-is him [subject-が] dislikes [because-ので].
An unusual two-clause structure where the explanation comes after the main statement, linked by というのは ('that is, the reason being'). ~そうだ here is the appearance reading of the auxiliary ('seems, appears, looks like'), distinct from the hearsay reading also written ~そうだ but with different attachment rules. ~ので marks the cause and is softer than ~から. 従う ('follow, obey') takes に, parallel to English 'follow to (the rules).' Note that 嫌い is a na-adjective and takes が for what's disliked.