First, sounds like a great trip that the kids will enjoy and remember!
Second, I'd echo the cautions of others here. Both with respect to 'that's a lot of trailer for a newbie with a 2500' and that's a lot of miles.
You might be more comfortable with something a little smaller, otherwise you might be worn out "white knuckling" it hours a day...that can be very taxing on your nerves and such that you dread the start of each road day and may not be able to make the miles you're planning.
Your family might be more comfortable with a shorter route where you travel only 200-250 miles per day with down days every few. I know my kids did not enjoy the scenery of the drive as much as I did, and unfortunately kids these days have electronics to avoid boredom.
Think hard about scaling back your aggressive dreams some, but regardless enjoy this once-in-a-lifetime family experience!