Don't miss the Old Faithful Lodge. It is a wonder to see all the log work. Since you are camping, if you can work it out, see if you can get a leftover cabin or room there for a shower one night. The plus side of that is that you can only get reservations in the lodge dining room if you are a guest. You didn't say how old daughters are; a bit older and they appreciate fine dining more. One of the best meals ever for the wife and me, complete with wine and dessert for a reasonable price. We have never made it to Mammoth yet. Thermopolis has an old hotel if you are so inclined with a private pool.
I am jealous.
I have not been to YNP for over 40 years when my Parents would take me as a child but in the dining room of the lodge I understand that one of my cousins made the art glass partitions for the booths after the big fire. I would like to go and see it all again...we used to stay in little cabins that were heated with wood burning stoves across the road from Old Faithful...saw it erupt many times.
