English Translation
The trees are planted three meters apart.
Could 離して also be replaced with the intransitive 離れて ?
@ericaw
The original Japanese sentence sounds very unnatural so as your alternative one.
3メートル間隔で木が植えられている。（さんメートルかんかくできがうえられている）
is the natural expression. Just memorize the phrase 間隔.
If you replace it with 離れて, that sounds that trees distance themselves from others (i.e. trees can walk).
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Thank you for teaching me new vocabulary! 
Would this sentence sound natural?
兵士は3メートル離して進んだ。
Sorry, but I don’t understand what you are trying to say. The only interpretation I can deduct from your sentence is:
“The soldier separated A from B by 3 meters, and then went forward.” (A and B aren’t specified)
I meant to say, “The soldiers advanced 3 meters apart.” How would I say this?
you replace it with 離れて, that sounds that trees distance themselves from others (i.e. trees can walk).
Would it be 兵士は3メートル離れて進んだ。? The soldiers are distancing themselves from each others, because they can walk.
Sent.#1: 兵士は3メートル離れて進んだ。
Sent.#2: 兵士は3メートル間隔で行軍した。（さんメートルかんかくでぎょうぐんした）
Sent.#3: 兵士はお互いに3メートルの距離をとりながら進んだ。（おたがいにさんメートルのきょりを…）
Sent.#1 (proposed by @ericaw ) is vague, and is more likely to be interpreted as “A soldier distanced himself 3 meters from a tank etc., and then advanced”. But still, the entire sentence sounds unnatural even in this context. There are two problems:
Please keep in mind that 離れる as an intransitive verb does NOT always mean that there are more than two same entities, and they are distancing from each other. Therefore, if native speakers just read Sent. #1 without the English translation, many of them assume that the subject is “a soldier” (singular), not “the soldiers” (plural).
離れて進んだ as a compound verb is also inaccurate. It sounds like “took a distance first, and then advanced” – two different actions were chronologically taken. But you wanted to say “advanced by keeping a 3-meter distance” – the main action is “to advance”, and “3-meter distancing” is not a pure action but a status (quasi-adverb).
Unlike Sent. #1 with 離れて, 間隔で in Sent. #2 has the connotation of “more than two same entities” are in a row. Also, I replaced 進んだ with 行軍した in order to make it more clearly stating that the subject is a group of soldiers (i.e. a troop).
Sent. #3 with お互いに + 距離をとりながら is an alternative. お互いに (each other) is clear enough to describe a group of soldiers. ～ながら means “while” or “doing A in parallel with doing B”. All the abovementioned problems are solved by Sent. #3. However, I still prefer Sent. #2. It’s much more concise.