Don't resort to force — appeal to reason.

Literal

Force [to-に] rely thing [is not-ではなく], reason [to-に] appeal [imperative-なさい].

~ものではない means 'one should not' — a principled prohibition rather than a situational one. 武力に頼る (rely on force) is contrasted with 理性に訴える (appeal to reason). The ~なさい at the end makes it a moral instruction.