1. A check of AGS-ATL flights today shows that none arrived more than 5 minutes late, with the exception of 5107 which leaves 4 minutes from now and is estimated to run 40 minutes behind. What flight # were you on?
2. Why was the flight you say was delayed delayed? Weather, air traffic, mechanical?
3. You are not due any compensation. If the delay was mechanical and you were stranded in ATL, you would have been entitled to a hotel+food, but not reimbursement for hotels in DTW.
4. As to the DTW hotels, I have never experienced a major city hotel which will not acommodate delayed pax, either through a refund or some other arrangement. But, you need to call the property (not the toll-free reservations line) ASAP.
5. Do not "invoke" rules, there is nothing for you to "invoke". The quoted section from DL's contract with you is clear that DL may at its option rebook you on another carrier. If it's still feasible, as for that. Not particularly likely that DL will do it, but a polite ask is OK.