Congrats on becoming a Dad!
I am the mother of a toddler who has been playing this game since Beta.

Of course, my motherly duties are my first priority so usually I'll play during nap times (and after bedtime). If my kiddo wakes up from nap while I'm healing a dungeon or something, then I'll let him sit next to me and watch YouTube on the other monitor, or I'll find him something to do right next to me until I can finish and log off.

I suppose my advice would be to make certain you actually have a good chunk of time to play before you log in, and when its time to log off... just do it. Try not to fall into that trap of "let me do one more thing....."