If I were to have a quote and there were a contraction in it, would I need to put brackets around the de-contracted word or can I just de-contract it.
For example: He said, “I’ll go to the store tomorrow.”
Would I de-contract it the first or second way in MLA format?
“[I will] go to the store tomorrow.”
“I will go to the store tomorrow.”
I wouldn’t de-contract it, as the contracted form is perfectly valid and understandable. But if I did expand out a contraction or acronym I would use .
Note that if something was said in speech, the  is not needed as it can validly be expanded as normal speech always leaves bits out (elides things) and we are not usually even aware of this. If the non-standard contraction is retained it is for effect. If a non-native speaker uses something in appropriate the choice is leave it (and mark it with sic) or replace it (and mark it with ) or rewrite it as an indirect quotation (and mark this by omitting the “”).
“I wanna go to the store tomorrow”.
in speech –> text for the first time “I want to go to the store tomorrow”
in text –> corrected text for MLA “I [want to] go to the store tomorrow”
in text –> sicced text for MLA “I wanna (sic) go to the store tomorrow”
but the  still seems a bit pedantic, and the (sic) a bit rude, to me personally.
I would either leave it or expand it without mark up if I had to have it as a quote, and if I had to have it, it means the form is important and I would leave it. Otherwise I would make it an indirect quote.