Don't suggest adding 5-6 hours on top of an already large trip.
My wife and I have recently returned from a trip from Texas. Before we left I recommended a trip to Kansas City to drop off our dog with my wife's parents. It made our trip easier, but it also added a lot of extra travel to our trip.
Besides the longer time in the car, and the fact that we did not make it to Texas until 3:30 in the morning, the fact that we were exhausted by the time we arrived and had very little time to sleep on our trip, lead to a tough trip.