My family and I took a trip on Southwest Airlines last weekend, and from the perspective of a parent traveling with small children, it was a big let-down. Gone are the egalitarian days when the first person who showed up got to board the airplane first and a family got to pre-board. Actually, gone is any concern for a family traveling at all.
At first there was just online check-in, so the people who thought to check in on the internet got on the plane first. But I guess they figured they needed to cater to business travelers more, because now there's special pre-boarding group (that you have to pay for I think). And the new rule is families get to board after the first sixty people board the plane (provided the family isn't lucky enough to have group "A" boarding passes). I guess the point was to keep families from taking the seats up front before the people who waited in line for boarding group "A" get a chance. But the point of family boarding is to give the families some more time to get settled. Southwest would rather have the families fight past everyone jockeying for overhead bin space.
And about the changing tables? On one of our flights there was no changing table at all, and on the other the only changing table was in the lavatory at the front of the plane. The problem is you can't wait at the front of the plane anymore (new FCC regulations). So you have to wait until the occupied light goes out, then race down the aisle of the plane, baby in hand, to get to the lavatory before someone who is sitting in one of the seats in front of you decides to get up to do their business.
Flying with kids is difficult enough. If you've got a choice, I would avoid Southwest.