、。
Since she dislikes him, she's likely to refuse to follow his advice.
Literal
She [topic-は] he [subject-が] disliked [because-なので], his advice [to-に] follow [nominalizer-こと] [object-を] [likely-to-refuse-拒みそうだ].
Several patterns to notice. ~なので combines the copula な (for な-adjectives like きらい) with the soft reason ~ので. ~に従う ('follow, obey') takes に for what's followed — advice, rules, instructions. ~ことを拒む is the standard way to express 'refuse to do' (refuse the act of). And ~そうだ on a verb stem (拒みそうだ) marks visual/inferential probability — 'looks like she'll refuse.'