"Subdue" means to quiet or overcome. "Suppress" means to conceal. Neither of these verbs is idiomatic with to+object.
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"Subjugate" comes form the Latin "sub" (under) + "jugum" (yoke), and it always takes the sense of one party conquering or bringing under complete control another party. This isn't to say that theHer personal ambitions had been subjugated to (= considered less important than) the needs of her family.