It sounds like you're beginning to recognize the triggers - and that's the crucial step! If you can avoid the confrontation all together then that's best. Otherwise try to understand what the trigger was so you can avoid / distract them before the escalation starts the next time. It was Tia and Jack that fought in my rescues - Peggy is so submissive that she keeps herself out of harm's way!! After a while I could see Tia start to tense up before she'd go for Jack, and I could generally diffuse the situation. When Jack started it, it was more unpredictable, and so less controllable.
Food is often a trigger for Tia but sometimes she will guard other things that are precious like a cuddle with me.
You'll be pleased to know that they got their differences sorted out, and now are really fine together. Tia will defend Jack if he sounds worried, and Jack follows Tia around like a lamb!
I find that mine are
more aggressive on the lead as they feel they can't escape if they need to. Tia and Jack major fights when Jack first came when they were on the lead - always initiated by Jack. He really can't cope being around other dogs on his lead!
When I give a treat, I say the name of the dog I'm going to give to and then give. They soon learned that as they all get one (when they've earned it), they just have to wait for their name.
Peggy will play with me, and the occasional other dog, but Tia and Jack don't play. Tia once played ball, but just to out do another dog. She looked at me as if to say - "well I can do this if I choose to, but I just don't choose to!"
Good luck with it all - it's hard work when they argue, but you'll all get there in the end!?!