Its crazy but with good planning it can be done. I go with my husband regularly between coventry and edinburgh, it's about 5-6 hours drive. Our best stop is tebay, it's clean and has good facilities. I've been doing this since kid number 2 and I now have 4 kids between 6yrs and 6 months old. 2 of them are Travel sick. since you mentioned a 5 yr old who is sick, you can get 'joyrides' sick tabs. They're tiny your child should be able to swallow it, does the job. I'm not Tavel sick but since travelling this far I have been, all the winding country rounds don't help. on our last trip my husband took a different route which meant we couldn't go to tebay but it was more motorway driving rather than country roads, and it was a bit quicker. I'm sure it was the a1 our usual route is the m6. The a1 was not as busy so we arrived slightly quicker, and less nautious.
Keep a bag of spare clothes for all ya kids within easy reach, because my son was sick too and he doesn't get car sick. avoid giving them liquidy food in the car or anything with strong flavours it can make it worse. Milk before a journey a big no no unless its an infant who lives on the stuff. biscuits lots of them good for the kids, sweets, especially boiled ones or lollies, water rationing lol.
We don't usually stop @ a hotel although I used to complain about it, I've just become accustomed.
If you can afford to stay the night in a hotel or b&b then do so it will take out the stress and hardship especially with the kids. If not plan it well. I think you should leave early, my husband is not a morning person but he agrees early is best because it usually gets busy around the Wolverhampton region, you can get stuck there. We usually leave @8am and arrive by 2.30pm. I used to leave earlier but since the kids have multiplied I need to chill or I will go crazy.
My nutty husband often travels further than London to buy products for his job, he doesn't stay over I couldn't do it!
Btw keep an eye on your tank there aren't many stations my husband overlooked it but luckily we went off motorway and managed to find one. Just makes your journey longer and the kids start whining.