If you can fly nonstop UK-Vegas and the Vegas-Hawaii that would be the way to go. Flying any other way means multiple stops which increases the time and chances of problems.
The UK- Vegas flights are about the same as the UK-NY flights. But from NY you still have another 5-6 hours non-stop to the west coast and then another 7-8 hours flight to Hawaii. Cut out the extra flight across the States and head to Hawaii if that is where you want to go. I would do this but especially if flying with children!

You can have stop overs in Vegas one way or both ways. Take a few days and see the Grand Canyon and Hoover Dam. Worth the time. If you allow a couple of days stop over you can easily book two separate tickets.