Two points with dogs,
1, when dogs walk or run, they twist their feet at the end of their stride, its the way their legs work. So even small dogs will rip and tear a lawn over an amazingly short time. And I am seeing trails along the fence and at the gate in your photos.
2, my experiance over 30 years being the head gardener at a 21 acre senior living center that allows dogs (they really do extend a persons life span!), has shown me that dog manure and urine will damage a lawn. Bare spots where the manure and urine is too concentrated and heavy growth where it's diluted. And again, I am seeing bare spots and heavy growth in your photos.
I'm not saying you dont have other problems as well, just dont discount the damage 4 small dogs can do to a lawn, I've seen it and been amazed at how quicklly it can happen.