It seems that there is no strong difference in the use of institute and institution in the English language. Therefore "the institutes" should be correct, or am i missing something?
Institución doesn't follow the default pronunciation rules, so it needs to put an accent on the "O" to show that it carries the syllabic stress. The plural form doesn't need an accent over the o, because using the default pronunciation rules the "o" is already stressed in that word. You see this happen quite a bit with certain plurals.
Your comment is three months old, so you might already know this by now, but I'm commenting for others who might see this discussion.
The default emphasis in Spanish pronunciation is the next-to-last vowel sound in the word ("in-sti-tu-ti-ON-es"). I believe there are a few exceptions, but generally, if the stress is on any other syllable (as in "in-sti-tu-ti-ON"), it needs an accent mark over the vowel that is stressed.