Motivation and coordination is key.
If you don't communicate with your wife and find a happy balance, mission fail.
My wife is just as much into endurance sports as I am. We have a 2yr old and an 8 month old currently.
In both cases, I found a "big" race to train for, and do, while she was pregnant. Get that out of my system per say. Then, once the child was born, I said "Ok, your turn to do something epic since you have been pregnant for the last nine months." She had her best if five Ironmans six months after giving birth! Amazing. And while she was training for her big races, I did smaller events that didn't require a ton of training and was quite content.
Second child was tougher.. because two kids is tougher! Still, she prefers AM workouts and I am lucky enough to have an hour every weekday at lunch. Then, I do long on Saturday and she goes long (bike or run) on Sunday. It generally works.
I will admit that I am not very motivated unless it's outside, in a fun place, having an adventure. I am not one to do a bunch of loops of the neighborhood and/or train indoors. I don't have that kind of discipline or motivation, unfortunately. For those that do, then there really should be no problem. There is ALWAYS an hour or so during the day to get something in if you don't mind using the treadmill in the garage, or trainer in front of the living room.
Sleep can be rough at first, but it really didn't change things for me. I think I went six months getting 4~6hrs a night with our second child.. it was rough. But I still went out and did it.
Never, ever hesitate to give your wife time to herself. Take on the kids as much as you can and let her do her thing. I always volunteer to hold down the fort for the day or evening so she can go out with friends. Do that and it won't make being gone for 2~3hrs on a weekend morning seem so bad.
-------------------------------------- Also worth nothing, more competitive white people prefer triathlons because Kenyans can't afford $10,000 specialty bicycles.