You got caught up in a large rationalization of flights, going on now at most U.S. carriers.
This is a similar thread.
http://www.flyertalk.com/forum/showt...=cancel+flight
Delta's not going to pay for hotels for a schedule change. The routine is to book you on another travel date. Frequency of service seems to be a problem in your case.
AA is not a partner. No way is DL buying you a ticket on AA.
Typical rescheduling involves DL making room (even to overlook award inventory restrictions and fare class restictions) to book you on their metal. See what DL operates in the relevant timeframe to your destination and ask for it. Or, get a refund of money or miles w/o fee.