Exception to this is, the group of dwarves referred to as Durins Folk (The Longbeards), who, based in Moria (Gundabad originally), had friendly relations with the elves, and did not war with them. (The freakin password to their door is in elvish.....)
In fact, during the second age the Dwarves of Moria were closer than ever with the elves....
The war between dwarves and elves was when the nogrod dwarves stole the silmaril, first age. There should be no mention of war between elves and dwarves in this series if its supposed to be second age.