You probably should check your reservation on aa.com to make sure that your secure flight and immigration data is in their system correctly. Many issues with flight data with all of the US carriers about getting the preflight stuff right especially when it's coming from another carrier. If aa.com says all of the data is ok then you shouldn't have any problems checking in with them for their leg(s). I had a similar connection this summer with both BA and AA on the same ticket. I just checked in with the operating carrier online at their normal times. Just make sure you use the right PNR for each system and sometimes you might get lucky and get checked in all the way through on the first leg. Check the second carrier anyway just to be safe even if you get a BP or two for those legs!

Of course with AA and BA YMMV!