The answer to your question would be that the correct way to punctuate this sentence is the following one: My cousin Amelia decided to transfer colleges after she found out her original school, Highlands University, did not have a strong, study-abroad program.
The NP "Highlands University" is an appositive phrase that renames the NP "her original school". That is why it is offset with commas, said appositive phrase does not provide information that is considered relevant to the meaning of the sentence. What is more, a comma is needed between the string of adjectives "strong, study-abroad" describing the noun "program". That is why this is the correct option.
