Kids and "their" pets.

I've had a revelation recently that has me quite bothered. I have been snookered by my family. In March of this year my wife sent me a picture of herself at a co worker's house holding a puppy. I knew right then that I was in big trouble. Her text spoke of how laid back and cute he was. I resisted, even when my little girl was told of the dog's existence. At that point, I had to realize that the dog was going to be living in my house. I asked who would take the dog out, and said it wouldn't be me. I made it known to my wife that this was going to be her dog.  I did NOT want a dog. We have a dog.
What am I doing out here!
So we have a min-pin Chihuahua mix that weighs about 11lbs. I realized a couple of days ago that I had been had by my wife and kids. I realized this when at about 11:30pm I was outside with this dog on a leash begging him to poop so I could go back into my comfy house. What the hell had happened? I made my position known before we even had the dog: I was not taking it out, ever! Yet, here I was putting the bowel movements annoying little dog before my comfort. Obviously my little girl could not take him out at that point in the night, but my wife had played the guilt card on me. "It's dark and scary out there" she told me.  So, it was left to me to make sure I didn't have to clean up pee or poop in my house. That's another thing I had mentioned before we got the dog. I was not cleaning up any messes in the house. Guess who cleans up any accidents? That's right, dear old Dad. How did this happen?
When is the right time?
So, that brings me to the question that has been bothering me for a while now. When is the right time for a family to take on the responsibility of new pet? My kids are 4 and 2, and I think that's too young to expect them to take full care of the dog. My wife on the other hand could, but somehow it's been left to me. I think that a dog(preferably over a cat in my opinion) is a good thing for a family to have. It does teach kids responsibility, but only if they are at the right age and ready. I wish that I had had a dog that grew up with me when I was young. My family had a number of dogs, all kept outside, but we lost them all to car accidents. We lived in a location that had a blind hill, and had four or five dogs hit as cars came over that hill faster than they should. I think that helped me learn about death and loss at an earlier age than most. I certainly don't want my kids to have to learn that just yet. Yes, I am bitching about having a dog, but I think my little girl is learning from having Rocket(we named him that after the University of Toledo Rockets, where we used to live) in our house. I had her take him out on his leash to go potty during the summer months, and she liked doing that. It was funny to see her struggle to keep up and be overpowered by the little dog! She has learned(I think) that it costs money to buy him food, and that he has to eat just like we do. So, I think that's good. However, for me to expect her to fully take care of the dog would be unfair. I think if she were a few years older I could expect more from her. At this point, I have accepted that taking care of this dog is my mostly my job.
So my question to you my dear reader is, when is the right age to get a family pet and expect your kid(s) to take care of it? I am really looking forward to hearing what some of you think as this is an interesting subject to me.
I look forward to hearing from you, and good night. Always remember, I did NOT want a dog!