While I don't get up at 430a, I get up at 530a.
While I don't have an hour and a half commute each way, I've got a 30 minute commute each way.
I get in to the office at 630a, and leave between 330 and 4p.
I've got the power rack and weights and dumbbells and bench and chin and dip stand in the basement.
On my workout days I enter the house, empty my cooler, and immediately get changed in to shorts and a t-shirt and descend the stairs to my gym for an hour.
After that, my evening is free for me to be with my family.
I've been working out in the home gym since 1999, when my daughter was seven years old. So she's thoroughly indoctrinated in to the routine. Both my wife and kid leave me alone, because they know that that's my time, that they'd rather not get barked at, and that Dad's a generally happier and calmer person after his hour in the gym.
We have a gym here at the office, but it's a selectorized stack machine that's a guaranteed joint wrecker, dumbbells up to 50 pounds, and a few bikes and treadmills and climbers. No barbells, no plates. So I don't work out in the gym here at the office. Also, some thing about sharing the room with a half dozen people yapping and mewing on the exercise machines, while the dumbbells lay dormant makes my stomach queasy.
But I do a couple of sets of deep knee bends and pushups in my office at various times during the day, which keeps me warm, stretched, and adds a teensy bit of volume.
That's just my solution. I've always been able, for the thirteen years of my daughter's life, to get a workout in a couple of times a week. Whether that meant picking her up at day care after the gym (and wasn't that interesting to pick her up, with her car seat, and diaper bag after a heavy deadlift day).
To me, reducing your commute, to a job you obviously don't enjoy (I know, it's why they call it "work"), is the solution. You've got three hours in your day when you're doing "nothing".
I live in Atlanta. I'm familiar with people who commute three hours total a day, every day. And how it creates issues in their lives. I know, I know, people in New York and L.A., etc. have commutes that are far worse than most of what Atlanta whines about.
Cut your commute, get a job you enjoy. Your wife and kid will benefit, as will you.
My wife has worked erratic and sporadic hours since after our daughter was born. Currently she owns her own business and works primarily out of the house. Recently she made the committment to join me in the gym when I work out of an evening. It's tight, the space is small, but at least she's doing some thing. So even with funky hours and busy schedule, it can be done.
You do deserve kudos for doing what you're doing however, no matter how frustrating. You don't need me to tell you that abbreviated workouts, that late in the day, are what you need.
Another suggestion (I believe this is from Tsatsuline's "Greasing the Groove" article)? Don't do your workout all in one push. Your wife sends you down to the basement for a can of tomatoes from the storage pantry? You have to walk past your power rack? Get a set of chins in; one on the way down, the other on the way back. Keep the bar loaded for squats or deads. Do a set of pushups or dips.