We live in Dallas and went to Aulani 3 years ago. We most definitely took the red eye over night flight from HNL directly to DFW. I would NOT stop in LAX as it just invites delays! My daughters slept almost the entire flight, and yours should too since teens can sleep almost anywhere! We got main cabin extra seats on the flight, which are coach but give extra leg room. In retrospect, I wish we would have sprung for First Class because then at least I would have slept some on the way home! Next time, we will do that.
Traffic in Dallas can be bad any time of day for no apparent reason, but it is universally bad from about 7am-9:30am and 3pm-6:30pm. So try to avoid driving long stretches during those times if you can. Sometimes it is unavoidable, and you just have to gut it out. I use Google Maps (my husband uses Waze) for my traffic app, and it is very good in Dallas. I put in where I am heading and just follow the prompts. The time of travel estimates are usually spot on. The highways are well marked and not super confusing, but a few areas around downtown (where the Sixth Floor is) are a little confusing. Just follow google!
Getting out of DFW airport can be a little weird because everything exits to the left (the opposite of most roads in the US which exit to the right). For you from the UK, this may feel very natural, but it can be very confusing to the US driver who is not familiar with the set up.
If you are flying home from DFW to the UK or your next stop, be aware that security lines can be very long at DFW, especially early in the morning on the weekdays, due to heavy business travel. If you are in First Class, most security points have a Priority Lane, so look for that for sure. Not sure if you can get TSA precheck from the UK, but I am thinking not, but if so it can save time if you go to one of those check points.
Have fun seeing some iconic Texas things! South fork is fun for a one time visit, and the Stockyards in Fort Worth just scream Texas. The Perot museum is a great suggestion, and the Sixth Floor is very moving. If you like art, the DMA (and Nasher sculpture garden, walking distance) is wonderful. Klyde Warren deck park is right there too, also walking distance. The Dallas Aroboretum is a botanical garden (much much more than trees) if you are into that type of thing. You can kayak on White Rock Lake near the Arboretum (near where I live!). PM if you need restaurant suggestions, etc).
At Aulani, we did the pools the last day and left our bags at Guest Services, with a small bag of our change of clothes for the flight home. They gave us a card for the Lounge to change in, but note that it is VERY small and packed with folks waiting for rooms to be ready, and when we went, you only got to enter once, so it was not come and go. Must have your change of clothes and toiletries ready on your entry at the end of the pool day. Have a wonderful trip to Aulani!