With those many concerns I do wonder if you really want a dog. Nothing you are saying is a major concern. I have never heard of anyone failing to house train a puppy yet. Very few dogs bite children and certainly not if the child is under control. Is your child well behaved or does he run riot. If you can train a child you can train a dog, if your child runs circles round you so will your dog. Of course your dog can be left while you go shopping. My dogs have always been left from day 1 for as long (within reason) as I need to. No one wants a barking dog so make sure that doesnt happen by keeping the dog happy and well balanced and building up the time you leave it for.
It does sound like you might be happier with a rescue dog that is already house trained, used to children and cats and fairly obedient. I am sure they are out there. It might be an idea to choose the breed you want and contact the breed rescue.
From what you say about your life style there is no reason at all why you shouldnt have a dog, and if you do things right the dog will fit into your family and your life and enhance it.
But if you are going to worry about it changing things or being a problem then maybe a dog isnt the right pet for you.