Refund from Delta for canceled trip

I'd like to know if anyone is familiar with any specific regulations that force Delta (a US company) to refund or give some kind of compensation to passengers that had their trip to the EU (AMS in particular) cancelled while already at the gate (I'm pretty sure there is a regulation regarding that inside the EU).

Specifically, the departure time was first delayed by one hour (two hours before planned departure), then was delayed again by two additional hours and in the end cancelled and reprogrammed for the next day. Note that my final destination was Rome and not Amsterdam, so if they had better communication with passengers, I would have reprogrammed the trip via another city on the same day with Delta, but the awful way in which they handled this made me lose enough time to make me lose this opportunity. This resulted in me and other passengers waiting long hours to be sent to a hotel with a voucher because Delta initially sent people to a sold-out hotel. As of now they just provided 17500 miles as compensation that I find inappropriate.

This is the claim I sent to Delta with more details of all the situation:

The trip is the one I booked with confirmation number XXXXXX and originally was booked to go from DTW to AMS on September 17, AMS to FCO on September 18, FCO to JFK and last JFK to DTW both on September 24.

The problems started when waiting for boarding to DTW to AMS segment. At the gate, a one hour delay for departure time was announced and that would have affected my possibility to actually get on my connection in AMS, because that was leaving after one hour and a half from the planned arrival in AMS. But the Delta people at the gate reassured me that there was no problem with that since a replacement pilot for our trip was about to come and then we would have departed just a few minutes late with respect to the planned departure, that was 6.25 pm. This didn't happen and the next thing we were told is that a new pilot was coming from Atlanta to allow us to depart at 9.30 pm. Anyways, a few minutes later than 9pm we were told that the pilot (for unspecified reasons!!!!) didn't come to DTW and so that every passenger would have been handed a voucher for a hotel night close to DTW, because the whole trip was being cancelled and moved to depart at 5.30 pm on the next day.

At this point, I tried to rebook my trip because I had to go to FCO, not to AMS, but the only trips available at that time were about to depart, so I didn't have enough time to rebook because the app wasn't letting me do that and wait times on the phone and at Delta customer point at gate 43 in DTW were too long. Please note that if we were given clear information at the gate, I would have been able to rebook my trip in time and go from DTW to FCO with arrival times very similar to my original trip.

Please note that all passengers were left at the gate for more than 3 hours with only some very scarce snacks and water supplies provided by Delta. Anyways, I just accepted that I was losing one day of trip at that point and went collecting my voucher for a hotel night, and I rebooked my trip to go via JFK on the next day (instead of accepting the rebooked trip via AMS). It was already past 10 pm when every passenger was handed the hotel voucher and we were told to go wait for the hotel shuttle in the parking area of DTW.

After collecting some of the passengers (about two rounds of passengers) the hotel shuttle stopped coming and finally a passenger was able to call the hotel to be told that it was sold out, meaning that Delta only handles vouchers careless of where people are headed. So we were lucky enough to find some Delta people at check-in desks (it was almost midnight) and they were able to change our hotel stay to another hotel, this time including a taxi ride. Things went ok with this one but I and other passengers ended up checking in at the hotel quite late at night.

In response to this terrible, appalling and somewhat offensive behavior from Delta, I was only given 17500 miles some days later, and this is not enough. What other options do you propose? I think a full refund of that segment of the trip would be fair.