"If not, she will become his wife."
Translation:Falls nicht, wird sie seine Frau.
Yes, "Wenn nicht" is possible as well. "If" can be translated as either "falls" or "wenn", with "wenn" being perhaps slightly more common or colloquial. (If "if" is used in the sense of "whether", it translates as "ob").
"Wenn" cannot only mean "if", however, but also "when". So a sentence such as "Wenn du kommst, koche ich etwas" can mean either "If you come, I'll cook something" or "When you come, I'll cook something". So you can use "falls", which can only mean "if", to avoid confusion in certain contexts.
falls = if
wenn = if OR when
ob = if (in the sense of "whether"); whether
Maybe I've been misinformed, but I was taught that if a conditional is used, like if, the dependent clause is always in the subjunctive voice. (I even notice that many Germans do this when speaking English.) As a result, I went for "Wenn nicht, würde sie seine Frau werden". Is this wrong then?
In short, "Falls nicht" is a subordinate clause, serving as short-hand for a condition stated previously, and thus requires the specified word order. If the "Falls nicht" clause were expanded, it could be something like, "Falls sie das macht, wird sie seine Frau" ("In the case that she does that, she becomes his wife"). The word order is the same as other sentences in which the subordinate clause comes before the main clause. If you wish to put the subordinate clause after the main clause, my contrived sentence would become, "Sie wird seine Frau falls sie das macht".