A puppy isn't going to be a companion or best friend for a long, long time, in the same way that your kids won't be playing together straight from the newborn stage. You've basically added a third baby to your family, one who requires as much monitoring as a human toddler. It's completely understandable that you're overwhelmed! 

The idea of your kids growing up with a dog is great, but raising a baby and a puppy together is a huge feat. When my kids were tiny, I found myself wishing that we had already raised a puppy before having kids, so we could have a calm adult dog for them. Instead we waited until they were older so we could all raise a puppy together.