We are affiliated with another bank in another town due to us being majority-owned by the same holding company. Our affiliate bank wants to use their bank account with us to allow their customers to transact deposits into their account with the affiliate through our bank. We basically take the funds and place it into the their account and then the affiliate bank will withdraw the funds from the account and credit the individuals deposit account at their bank. As an auditor this is raising all kinds of red flags with me, especially in regards to internal controls. Are there specific regulations or laws that prohibit this type of activity that I can quote to management?

Sounds like you'd be operating one bank as a branch of another. (By accepting deposits at that location.) It's one thing to cash their checks - taking a deposit is another.