I've been having the exact same issue, and it only ever occurs with my escort ships. As soon as the ships are given a move order, or literally anything the make them stop escorting you, the cease fire immediately. But as soon as you call them to escort you again (i.e. for a jump), they open fire on each other again. It's as if they each see the other as a threat to their escort target, despite them both protecting the same ship. I have lost a rather expensive combat destroyer to these civil wars, and I hate having to fly solo with no wingmen.
IMO this could be fixed by not allowing ships to target other ships that belong to the same player/faction, under any circumstances.