I understand that you want your children to have the experience of having a dog. Not being an animal lover myself, I am content with our goldfish who require little attention and if I miss a feeding the consequences are not great.
Here's the thing, if you want a dog then you need to take care of it. It needs to be trained - specifically, it needs not to poop in the house every damn day. If you do not wish to train your dog, then don't bring it to Mom's house where it continues its excrement throughout the house. Also, if you see the dog eating styrofoam, stop it, instead of shrugging your shoulders and walking away. It's your damn dog, eating styrofoam does not agree with it, and I am tired of finding poop throughout the house. As you are nearing forty years of age, I can not seriously believe that I have to hold my tongue on this topic.
Besides your dog, it has been good to see you and the kids.