Conducting research at my alma mater
Since the other university is actually the subject of your study, then I think that the IRB of your current university is the better place to judge it. It avoids a conflict of interest within the other university. 

Your former colleague at the other university probably shouldn't be a co-researcher, but could be integrated into the study in another way; say as a source of information. This lets them, also, avoid a conflict. 

Proposing it to the Dean at that university may also be problematic. Your "want to help them fix the problem" will very possibly not be well received. You might get quite a lot of blowback. 

If they recognize the problem on their own and come to you as a consultant, then it is a different story. Otherwise you will come across as an unwelcome outsider and a disgruntled alum. 

I won't recommend against your study, but I think that you should keep it as independent of the other university's administration as possible.