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I'm having trouble with the order of "途中の商店" in
"ふと途中の商店街にあるパソコンスクールが目にとまりました".  
Shouldn't it be "商店の途中"? and that にある confuses me even more. How can I
interpret this sentence?

The entire sentence is:

> 「どうしよう。。」悩みながらとりあえず、近所のスーパーに買い物に向かうと、ふと途中の商店街にあるパソコンスクールが目にとまりました。

And the translation is:

> “What should I do?” I was thinking to myself worryingly, as I set out to do
> some shopping at a nearby supermarket when I came across a computer school
> in the shopping arcade on my way there.
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meaning particle-の
What's the word order of the nouns in this sentence?
>
> 「どうしよう。。」悩{なや}みながらとりあえず、近所{きんじょ}のスーパーに買{か}い物{もの}に向{む}かうと、ふと途中{とちゅう}の商店街{しょうてんがい}にある
> パソコンスクールが目{め}にとまりました。

First, in this passage-like sentence, there is nothing incorrect, unnatural or
illogical; It is just plain good.

> I'm having trouble with the order of "途中の商店"

But it is 「途中の商店 **街** 」, and not 「途中の商店」.

The 商店街 ("shopping street or area") is located somewhere between where the
speaker was and his/her destination, which is a supermarket.

And the computer school is located in that 商店街. 「にある」 just describes the
location of the school. Are you following so far?

「ふと」 modifies 「目にとまりました」 and nothing else. ←← This is the only part that was
not translated literally in the translation you provided. In the original, the
subject of the verb phrase 「目にとまりました」 is 「パソコンスクール」 (" ** _the school caught
my attention_** "). In the translation, however, " ** _I came across ~~_** "
was used instead and that is good translation. That happens all the time in
translation between two linguistically unrelated languages like Japanese and
English.

「途中の商店街にあるパソコンスクール」 is a relative clause. Perfectly natural, grammatical, etc.
「途中の商店街にある」 modifies 「パソコンスクール」. You must get used to this word order in
Japanese. In English, "the computer school" would come first as in "the
computer school (that is) located in the shopping area on my way to ~~"

Thus, the translation you provided is of high quality though it is not 100%
literal TL. You can trust it fully in learning the meaning of the sentence, if
not the exact structure of the original.
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About にある, に is related to 商店街, so it is 商店街に+ある.

ある is 連体形 (attributive or predicative inflection base in modern Japanese).
Whenever you see a verb in 連体形 in the middle of a sentence chances are that it
is used attributively (as a modifier of the subject or an object).

A general formula for translating:

Japanese: **verb in 連体形** + **主語** (subject)/ **目的語** (object)

English (both orders are possible):

**subject/object** + **past participle of the verb**

or

**past participle of the verb** + **subject/object**

In your example the verb is ある and in the context could be translated as _to
locate_. In translation the past participle _located_ is omitted for stylistic
reason but is implied: "a computer school _(located)_ in the shopping arcade".
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