First of all congratulations. My advice, for what it is worth.
Just go easy while you all settle in and learn how to deal with sleep depravation. We have had 4 kids, none of them have been sleepers. Even in the early stages they didn't even have daytime naps.
Now the youngest is 3 and we get a couple of nights a week where they all sleep through.
As for training, just remember anything is better than nothing, so even if you do a couple of whole body workouts a week or when ever you can, it will still be good for you.
My first couple of years as a dad, I lost about 30lbs and never thought it would come back. Time will sort it out, so for now, help your wife, love your kid(s) and do what you can.
I always say, "worry about what you can do, not what you can't do"
Our eldest is 11 now and I back training Ok and my wife is back competing as a figure pro, better than before. It can be done.
Best job in the world is being a dad, so enjoy it brother!