My wife and I hammock camp together.
We've found it's pretty much impossible for 2 to sleep together in 1 hammock.
My WBBB (warbonnet blackbird) 1.1 (fabric weight) DL (double layer) is perfect for cuddling/snuggling, but it's just too tight for comfortable sleep. We weigh together ~270.
We've ended up getting her a WBBB 1.0 DL as well, and an extra tarp so that we can sleep a bit apart if there isn't an ideal "triangle" of trees to set up under the same tarp.
As far as the dog goes (I don't have one), my only concern would be claws in the fabric. It is rip stop, but a large enough hole + weight of occupant = you're suddenly sitting on the ground with a large ventilation hole on the bottom of your hammock!.