Personally when I get into a fight of that sort with someone I'm incredibly close to, I always hate it not because we were fighting (that's totally natural on occassion), but because I can never assign blame. I know them so well that I can see, but more importantly UNDERSTAND their side of it, and so I find myself with no choice but to throw my hands up and say "its both our faults, and neither one of ours", apologize, and move on, never really getting that feeling of resolution from knowing that I was either right or wrong. It's so easy to fight with acquaintances, or people online, because you never have to truly live in the other side of the argument and so you can easily decide you were right or not.
I feel like as long as the love is there within all the fighting then it's okay, and even easy after a short time, to let an argument fade away without ever having resolved it.
I realize I don't know you all that well, nor do I know next to anything about your relationship with Gillar, so I hope this doesn't seem imposing. Just throwing in my two cents
Side note- here's a picture of a cat that's entirely too happy to be underneath this dog's ear. I smiled at it, maybe you will too.