I'll agree I think you can do better. I like the suggestion to run your itinerary backwards altho I don't drive in England that suggestion makes sense to me.
With the kids, I'd also probably cut Canterbury, Dover and Beachy Head.
I loved Canterbury (the town and the cathedral) and enjoyed the castle at Dover very much (did it as a day trip from Canterbury on a Rick Steves tour).
I rode along the coast to Beachy Head which I thought was a disappointment even though I was looking forward to seeing the "white cliffs". I'm not sure the kids will get much out of this. The beach is shingle (rocks) and was very crowded on the day we were thru there.
I'd give yourselves 2 nights in Bath and 2 nights in Salisbury. Are you planning to do Stonehenge? I love to visit it altho there are many on the forum who think it's not worthwhile. I find it an easy visit from Salisbury via local bus route which runs all day. It might work to do 3 nights in Salisbury if Portsmouth can be done as a day trip from there. (I've not done that so perhaps someone who has can confirm.)
Try to work your night/s in Bath so it's not the weekend. Prices go up and often lodging places will require a 2 night stay if you are booking on a Friday or Saturday night.
Remember 2 nights in one location give you a full day to see the sights in that area. Even thought distances appear short, drive times may be longer than you anticipate.