I didn't see your thread when you first started it, so it's probably a bit late for this comment, but may at least help others who are going through similar.
They always promise the earth when you're about to leave. All those things you were begging for over the years, suddenly they can find it in themselves to do it after all. Instead of this being a reason to stay, I regard it as double reason to go. He knew what you wanted all this time but just wouldn't go there, although it made you miserable. Now he is prepared to do it because he will lose out if he doesn't. Does that sound like a partner who really cares about you as a person, about your needs and happiness? Or like a deeply selfish person who will do just enough to keep his lifestyle intact?
I was unimpressed with the plan to drag a dog into this, too. A living creature with its own feelings and needs, and the emotions of the children who will likely grow to love it, being used as a tether to keep an unwilling wife in place. That's what that's all about.
Once before you were going to leave and were persuaded not to: what changed? Why are you still dissatisfied if he learned from his mistakes and at least honestly tried to improve? And what will improve long-term if you stayed again? I am so glad to hear you weren't fooled a second time.
Hope your new home is full of joy and love. I expect the STBX will find a new housekeeper soon enough.