説得にかかる vs other ～にかかる expressions

Question

母さんはそれから粘り強く俺の説得にかかったが、最後に折れたのは母さんのほうだった

Mom tried tenaciously to convince me(stop my foolishness), but in the end she was the one who gave up.

Reading this at first, i would have read it literally as "mom got caught in my persuasion" or "she got convinced". But with this sentence structure with the ～が、最後に... construction, that wouldn't make sense with two agreeing ideas in a row. So i looked up the expression.

説得にかかる: 人がある行動を行うのを阻止すること

compared to other ～にかかる expressions i can recall:

網にかかる: 相手の意図した通りに動かされてしまうこと/ 誘惑などに簡単に引っかかるさま

or

手にかかる: その人に処理や操作をされること

Why does 説得にかかる end up interpreted in the active voice while the others are in the more intuitive passive voice?

Answer 1

There are many meanings for かかる, just like there are many meanings for words like take, make.

説得にかかる falls under this usage type (start doing, work on):

その作業をする。取り組む。 《掛》 「三人で－・ってやっと運べるほどの庭石」

（動作性の名詞や動詞の連用形に助詞「に」の付いたものを受けて）その作業を始める。手をつける。着手する。 《掛》 「今日から印刷に－・る」 「反対派を押さえに－・る」 「ビラをはがしに－・る」

網にかかる falls under this usage type (get caught):

仕組んだものに捕らえられる。 「大きな魚が網に－・る」 「わなに－・る」

手にかかる falls under this usage type (be handled):

ある人の扱いを受ける。 「彼の手に－・るとオンボロ車もピカピカになる」

Answer 2

かかる, just like its counterpart かける, has a bunch of meanings as one of basic verbs. The usage you see corresponds to definitions below:

16 攻撃的に挑む。攻めていく。「束になって―・る」「攻略に―・る」

17
㋐物事に着手する。しはじめる。「仕事に―・る」「取り壊しに―・る」
㋑その事に当たる。従事する。「今―・っている仕事」

かかる is an intransitive that certainly is, as you said, apt to be interpreted as passive. But while its core meaning is around "be hanged on; be put on", in the definitions above it means more like "stick oneself on", or practically "engage in". In this sense, it is no more counterpart of かける (I can't imagine how to replace it with かける in those situations).

The nuance of this type of かかる is similar with that of "grapple with", that suggests the object is some relatively tough, or time-consuming task, or a potentially confrontational opponent. So your translation is fine.