I could do it but a few things I would need to be factored in.
How good is the car? I think if I was going that far, I would rent a car so if it broke down, someone would come get me with a new car.
How much time do you have for vacation? With that kind of distance I would like to see some of the stuff I was driving past. I would say if I didn't have 3 weeks to devote, I probably wouldn't go. This year we are driving and it is roughly 1300 miles each way for me. I'm taking 2 weeks.
Do the kids have things to entertain them? We drive between NY and NC alot and Redbox has become our friend.
Have the kids ever done any long trips? If they haven't done any 1+ days driving before, I would hate to make this kind of journey the first time. My girls have been doing long distance travel (not the kind your talking about) their whole life. But I have cousins who are a nightmare in the car just after 3 hours.
I'm sure you know what you and your family are capable of. If you think
YOU can do it, then you can.