Be careful with airfare: the $59 fare from Southwest is unfortunately NOT INCLUDING the additional fees for unaccompanied minors. SW flies bags for free but they still charge ($50 each way, I think) for unaccompanied minors. Ridiculous, in my opinion, but that's a rant for another time!
I think you should look seriously at Lesley's suggestion to have your husband fly out to them when you and your 3 kids are in TX. It might actually be smoother that way....taking a teenage girl outside of her comfort/safety zone (i.e., her home) to deal with something that is emotionally charged for her might just be a recipe for disaster. She may be more open to working to build a relationship with her dad if he comes to her and meets "on her turf".
And I disagree and take issue with the mom who called you selfish. A note to her and others who would post similar things: The role of mom and wife is hard enough without us laying judgement and guilt on each other. What works well for one family may not work well for every family.