Translation:Do you go to the college or the university?
It could be confusing in the case of Trinity College (the only constituent college of the University of Dublin) or the “recognized colleges” of the National University of Ireland, but many secondary schools in Ireland are also called “colleges”. On the other hand, numerous Irish tertiary schools are colleges in all but name, such as the several Institutes of Technology.
It's not grammatically wrong, but it isn't a translation of the Irish sentence.
"Do you go to the college or to the university?" suggests a "which" question, whereas "Do you go to the college or the university?" implies an "either" question, though intonation and context could be used to imply these different meanings with or without the additional "to".
In America, a university might call itself a college, but a college should not call itself a university unless it is one. Locally, someone might be referring to the two-year community college, which is definitely not a university, or the state university, which is. When we say, "Do you go to college?" without an article, it could mean either.
"College" is a somewhat non-specific term, somewhat like "school". A University can be made up of different "schools" or "colleges" ("the college of Medicine", the "school of Engineering", etc). The National University of Ireland is comprised of University College Dublin, University College Cork, NUI Galway (formerly University College Galway), Maynooth University, and the Royal College of Surgeons in Ireland. Trinity College Dublin is "the sole constituent college of the University of Dublin".
While "college" is usually associated with 3rd level education, in Ireland, many 2nd level schools also use the word College in the name.
Are you using the website, or are you using one of the various Duolingo apps on a mobile device? If you are using an app, and it is clearly doing something wrong, you need to take a screenshot that illustrates the problem and submit a bug report
This is a bug, rather than a problem with the Irish course, because the web version of Duolingo accepts "Do you go to the college or the university?" as the correct translation. As such, you might be better off posting in the Troubleshooting forum, where there is some chance that a Duolingo developer might see your post (I can pretty much guarantee that there aren't any Duolingo developers reading comments on Irish exercises).