Congratulations on your new puppy! At this point it does not matter where he came from. He is yours and he is counting on you for love and care, and from ths sounds of your enthusiasm, he is one lucky little guy to come to your home!
Immediate advice from my perspective is just to make the puppy feel secure and well loved. Put his crate next to your bed at night and let him lick your fingers if he is lonely. He should settle down fine if he's fed and has gone potty and is tired from a busy puppy day. If he wakes up in the night, take him out on a leash to go potty. Give him a treat if he goes, then return him to his crate, again with a treat and a kind word. If he cries, let him lick your fingers. He should settle down again. It should not be much more difficult than that!
During the day, keep him confined to a puppy proof area, easy to clean up if he has an accident. Ideally you want to prevent accidents by taking him out to potty often, and especially at key times such as after playing, after eating, and upon waking. Puppies can't "hold it" very long. As you get to know him, you'll notice small behaviors he does just before he needs to pee. Pick him up and take him out before he pees! Don't scold him if he makes a mistake peeing inside. Its not his fault. He just needs to get the correct pattern of where to go, and that's the owner's job to help him repeat success after success. Always praise him lavishly when he potties outside and give a treat too. Housetraining can largely be accomplished in a couple of weeks if you are very attentive and consistent. Seeing as you have a baby human to look after too, there may be more "accidents" so it might take a little longer, but you'll get there!
Other things to watch for, make sure you are right there when your pup and your two year old are interacting. Puppies have sharp teeth and they don't at first understand how delicate is human skin. Puppies play using their mouths/teeth, so you have to expect some issues there until the puppy grows up some and learns to be more gentle. Likewise, two year olds tend to "pat" puppies in a way that a puppy may interpret more like hitting, so you need to teach each of them how to be gentle with each other. IMO the approach to teach this to both beings is to model gentle calmness and "set the tone" by being what you want them to be. There are other more specific techniques no doubt others will expand upon, but I think it all starts with your "aura" as the household leader.
Please feel welcome to come to the forum for specific advice as things progress. There are lots of great resources here.
Enjoy your puppy. They are little for such a short time. I believe you cannot love them too much. Set some reasonable boundaries, remembering that a puppy is just a baby, like your own human baby, so gentle guidance is the best thing, not expectations for perfect behavior from the start.... think shaping over time, just as you would do for a growing human child.
Most important at this time is making puppy feel safe and secure. Just like with a human child, you will get the most confident adult with a safe and nurturing puppyhood!