Don't just give away the dog behind his back.
DO sit down with him and say, "I appreciate that you like the dog and want to keep her, but let's go over the logistics before we make a decision. Together."
Then you can talk about how much a dog costs (food, vet visits and shots, emergency fund for unexpected vet expenses, toys, etc.) vs. how much room you have in your budget; you can talk about time management with the kids and with a dog; you can talk about how unfair it is to leave a dog in a kennel all day.
If he refuses to listen, then you have to be straight with him: "Look. I understand that you like the dog, but having a pet is a real hardship on our family, our workload, and our finances. You didn't consult me before you brought the dog home, and you aren't listening to me now when I'm telling you that I am not happy about keeping the dog. It's gotten to the point where I'm extremely resentful to you, and I'm nearly at a point where I want to tell you that it's the dog or me. So we need to fix this, otherwise there's going to be a problem."
You may also want to book a marriage counseling appointment.
I am willing to bet that this isn't the first time in your marriage where he just bulldozes your feelings/requests and just does whatever the hell he wants, right? You suggest that he doesn't help out enough around the house, and doesn't pay attention to your budget. So it's unreasonable of you to expect him to change his ways now, with the dog. YOU married him, so don't act surprised that the irresponsible guy is acting irresponsible. So either fix it or leave.