John Keegan is the man you are looking for. He has written a number of good books covering warfare and war through the ages. And he tends not to cover massacres and atrocities so the works aren't graphic.

I would go with what Warband said--John Keegan. He's an excellent author.

You could try Antony Beevor. The only problem is when he's not talking about politics of WWII, it gets pretty graphic. He wrote a book about the Fall of Berlin and he spends chapters describing the horrible atrocities and rape towards the German people. You could also try: Adrian Goldsworth (I think that's his name, been awhile) who writes great books about the Roman army and certain Roman wars. Right now, I am reading Robert L. O'Connell's "The Ghosts of Cannae", so far it's very good and does a great job desribing pre-war tensions and army set-ups. The only problem is...he's talking about Cannae so I would expect it to get graphic. Depending how old these children are and what their parents are like, I'm sure they could handle the gritty truth if you toned it down--you are talking about war after all and I think it's important they know that war is a horrible, graphic thing. That's opinion though, not fact.

How old are the children you are reading these military history books to?

My recommendation would be War by Gwynne Dyer. His work is written in fairly simple language and covers the changes in weapons, logistics, strategy, and tactics from the Battle of Megiddo to the Battle of Baghdad.