This is a great take on what we are leaning toward. Love the fact that it's long and rectangular. That fits the site well. The background that the dogs sits on looks like a window. It would be good not to box that in. The environment could be larger and more blue and white contrast. The lines are good and I see what you are going for but don't be afraid to go more organic. Maybe this would work if the entire logo were outlined and the background was behind the whole thing? The "run on mighty pup" would be in the grass and need to stand out though. Proportions are good too.
This is very close, but the grass blades make the text under ROMP almost unreadable. Overall it feels a bit constrained and crowded. I'd let it breathe a little more and lose the outline around the entire thing. It would work if it were simplified a bit.