Julie,
No, our flight is not non-stop. We change in Phoenix. Dh flew over 100,000 miles with America West last year and never had any probs. He said sometimes they were late coming into O'hare but so is every other airline he has flown. We even flew to Maui in November using America West and their partner Hawaiian airlines and travel was easy and no problem. I guess he/ we have always been lucky.
I would be upset if I were lap3 though and had to run with two babies through an airport. I have been there too. When I was pg with #4 I and my children (then ages 6, 5, and 2) flew to meet dh at one of his jobs and we had to get off the plane, re-board, and then sit at McCarren for two more hours after we reboarded in our seats as we had pulled back. Can you say N-I-G-H-T-M-A-R-E! That caused us to be on the plane six hours vs four. My two year old was not a happy camper just sitting in his seat! I had to use every trick in the book and he was still unimpressed. I have never flown with kids without dh since. That was America West too but we were delayed due to weather in Chicago.
Good luck in your decision.