From a recent inductee, welcome to the New Dad Club!
If you two anything like my wife and I, you will soon simultaneously have the same thought - "It's so good to be home. ... I can't believe they let us take them home! ... Now what?"
This, of course, will followed at some point by a moment when you're sitting alone in a quiet room with them and realize that this is your life from now on. THAT, for me anyway, was the best feeling in the world. Still is.
Best wishes to you and mom.
I'm still in the hospital, but I do enjoy how they can be so fussy laying down, but pick them up and they fall asleep in 15 secs.