It's quite possible that you can earn the points as you describe. The official answer is to read the Terms and Conditions for each offer, which should indicate whether that offer can be combined with other offers. Frequently, even if an offer says it cannot be combined with others, it can--but not with other offers that say they can't be combined with others. Confused yet? The best way to find out is to finish your stay and see what shows up in your account!

Does the AAA offer say 1000 points for each of the first three stays, or for completion of the first three stays (not nights)? If it's the latter, you might not see the 1000 points until your third stay.

BTW, let me know where the management is giving away free points!