I don’ t know of any children’s books. The only other countries involved were Spain and France. France declared war (again) on Britain during our War of Independence.
I’d suggest educating yourself with adult materials so you can fill-in the gaps orally until they get older. Knowing which MPs supported the Americans-or at least thought it best for England to make peace with us- and which didn’t is good to know.
B. Franklin was in England for long time periods up till 1775. Perhaps reading some of his materials could give you insight. http://www.revolutionary-war-and-beyond.com/benjamin-franklin-trips-to-england.html
Edmund Burke speech: http://www.let.rug.nl/usa/documents/1751-1775/edmund-burke-speech-on-conciliation-with-america-march-22-1775.php
Age of Revolution by Churchill, perhaps for a different perspective.
http://www.bbc.co.uk/history/british/empire_seapower/
Maybe select chapters from books at Heritage History of England, France, and Spain. Though, I doubt you’ll find much. They all had their own problems and I believe the war with America was viewed with a yawn, an inter-family/Empire squabble (like Britain’s with Scotland and Ireland), until we won. Then the War between England and France (and Spain) was on again and then the French Rev came, so there was a lot going on.