You will have to face the facts and decide to stop frequently. Kids have no awareness of time and they just know they are being forced to sit for extended periods of time. We take lots of roads trips and have since the kids were 1 and up. They are 3, 7, 7, and 10 right now. We travel with myself, my hubby, my BFF, our 2 grandkids ages 4 and 7, and my BFF's kids ages 7 and 10. When i plan the trip I look for parks, McDonalds or other places to eat with playgrounds, any type of business that caters to children.
Kids need the activity after sitting for even 2 hours. When the kids were younger we stopped every 2 hours for potty breaks and either a meal or a snack and play time. It kept everyone sane and gave everyone the opportunity to stretch their legs. For example, driving from OKC to Tulsa, a 2 hour trip. We would get on the turnpike heading East and the planned stop would be at the midway point at McDonalds. The kids could get out and potty, the adults could move around too, the kids get a snack, and off to Tulsa. When reaching Tulsa the first stop is a bathroom and running around area. It can be a park that has a playground or just a grassy area.
If I was planning atrip across country I imagine we would do some driving late at night when the kiddos are asleep but still, everyone will be cranky the next day due to not getting good sleep and their bodies would not be rested very well. I would only do that on a trip that was like yours. One day to a certain point then stop overnight then drive the next day until we go there. But plan on a lot more time due to the stops.
Just imagine what your baby will be feeling after 19 hours of being strapped to his/her car seat and not being able to sit up and do anything. She/he needs to have frequent stops to get up and move around.
Just plan it out, plan stops, take activities, plan on moving around in the vehicle so you can spend time with each child and play with them, like coloring with the 3 year old, they would enjoy that. There are many things you can do to lighten the travel stress to them.
There are a lot of sites that give good ideas too, I have them saved in my favorites, well, the ones I thought had the best solutions/ideas for us. Here is what yahoo search pulled up when I searched for planning a road trip with kids.
http://search.yahoo.com/search?ei=UTF-8&fr=crmas&...