My experiences are similar. Nothing wrong with flying on two separate tix. I frequently do it with Int'l tix - find a good deal from LAX to LHR and book it. Then I wait to find a good deal from DEN-LAX.

As long as both tix are on one airline or within one alliance (all One World), I've never had any trouble checking bags all the way through. However, if you are traveling on two different airlines (non-alligned), then I've heard of them being unwilling to check if all flights weren't on the same PNR.

If you're all on AA and finsih one way of the 1st trip before starting the 2nd trip, you should be just fine.