现代汉语描写语法 page 233:
[the "了" character for expressing completion] 位于单音节的结果补语与所带的宾语、趋向补语及其所带的非可控宾语之间。
This descriptive rule is quite hard to read. Let me break it down.
Consider the phrase 拧紧螺丝 (tighten the screws). In this phrase, 拧 is the verb that describes the action of tightening the screws. 螺丝 is the object of the action 拧. 紧 is the resulting state that 螺丝 achieves, after the 拧 action completes. In Chinese grammar theory, we call 紧 the 结果补语 (result complement). Notice that 紧 only has one syllable.
Now the first part of the above rule says: If the result complement has only one syllable, then place 了 between the result complement and the object. Hence 拧紧了螺丝, not 拧了紧螺丝.
In your question "停在了离小岛不太远的地方" has a slightly different structure. In this case "在离小岛不太远的地方" is a preposition phrase that describes the result of 停, hence a result complement. Within this phrase, "在" is the preposition and "离小岛不太远的地方" is the object of "在", not the object of the verb "停". Nevertheless the above rule still applies since 在 still has only one syllable. Hence 停在了, not 停了在.
The reason that the rule emphasizes "one-syllable" is that, if the result complement is an adjective with multiple characters, we usually don't add 了 with object after the adjective. Compare 关紧了大门 (correct), 关严实了大门 (unnatural), 把大门关严实了 (correct).
The second part of the above rule is slightly more complex. It concerns another class of complements called 趋向补语 (direction complement). They describe not the result but the direction of movement. Typical examples are 游来了一群鱼, 带走了一本书.
Now notice that there is a difference between 游来了一群鱼 and 带走了一本书. In the first phrase, 一群鱼 is syntactically the object, but also the entity performing the action of 游, hence in fact the subject, and we can rephrase it to 一群鱼游来了. In the second phrase, 一本书 is the object of 带走, and we cannot rephrase it as 一本书带走了. We call the first case "非可控宾语", while the second case "可控宾语".
The second part of the rule says, if a direction complement has a 非可控宾语, then 了 should be placed between the direction verb (来, 走, etc.) and the (syntactic) object. Hence 游来了一群鱼, not 游了来一群鱼. Note that if we restore the object to the subject location, 一群鱼游来了, then 了 can be placed between the verb and 来, as in "他舅舅连夜跑了来".
Finally, if the object is 可控宾语, then there are two acceptable places for 了, as in 带走了一本书 and 带了一本书走.
