I was looking for the meaning of the verb (とどめる) and how it differs from (とめる). I understood that (とどめる) means (to stop "potentially" from moving). But how does that meaning relate to the following sentences?
１．家族を郷里にとどめたまま、兵役に出る。
２．事件の一部始終を記録にとどめる。
３．被害を最小限にとどめる。
The basic meaning of とどめる is, as 大辞林 would have it,
①動いているもの、動こうとするものをとめる。抑止する。「足を—めて眺める」「席を立とうとするのを—める」
Roughly, "To stop something or someone that is moving or is trying to move/about to move. To deter."
The various other common meanings/usages of とどめる can be seen as extensions of that basic idea of holding or fixing something in place and thus preventing it from moving, or from transgressing some limit.
From 大辞林, again:
②滞在させておく。残しておく。「家族を郷里に—めて単身上京する」
③あとに残しておく。この世に残す。「議事録に—める」「記憶に—める」「足跡を—める」
④その状態のまま残す。「現職に—める」「原形を—めないほどのこわれ方」
⑤（「…にとどめる」の形で）ある範囲内に限定する。「誤りを指摘するに—める」「出費を最小限に—める」
Your example sentence 1. corresponds to definition ② above, your sentence 2. corresponds to definition ③, and your sentence 3. corresponds to definition ⑤.
とどめる is the final blow!
But otherwise, just look up a dictionary:
とどめる (v1,vt) to stop; to stay (e.g. the night); to cease; to put an end to; to contain; to keep (in position, in place); to limit; to record (e.g. a fact); to retain; (P)
