Being a father of 2 kids in the same age range and having been switching from an on-site job to a home-office for the past 2 years, I can relate a little bit...
Exhaustion Comes With the Job
I don't think there's anything wrong with your friend's state of exhaustion. It's a known issue for all parents.

At the time of this writing, I haven't had a refreshing holiday or even a week-end in more than 4 years now. There weren't many occurrences of these events to begin with, and they weren't relaxing or refreshing or replaining. I'm not saying I haven't had a fun times, but they all left me even more depleted than I was prior to these supposedly "relaxing" times. You either are full-time parenting, or fixing things that have needed to be fixed for, well, the times before the first pregnancy (you know, that distant memory of a life you had), or you do whatever thing you have to to do, but you don't really kick back and relax.
Occasionally you manage to have both kids take a nap at the same time and you indulge in your own nap-time or maybe attempt to read 3 pages of a book before you doze off, but it's only to then feel guilt because you haven't done anything useful with that "free" time instead of using it to relax. It's normal, it comes with the "job", and obsessing over it just makes it worse. So your friend should just embrace it and accepts it's how things are now: it makes it a lot easier once you get there.
Or Does It?
It doesn't have to feel that way though. It's hard to snap out of it, but it's up to you really to make things work right.
It's up to you to:
- make time for yourself, your partner, and your kids;
- enjoy these times instead of suffering from them.
You Can't Really Run And You Can't Really Hide
Also, while I don't think I ever experienced the desire to go to work to get away from my kids, I'admit that I did occasionally feel that way when time came to leave the office: I'd think that staying later at the office was actually less tiresome than going home and having to deal with shopping, sorting out the mess, putting them to bed, etc... Because it honestly was less tiresome. But, it's also not a fair thing to do to my significant other who was either at home with the kid ("only" one at the time) or coming home from uni. You can rationalize it in a number of ways ("I did that many shopping days, bed-time stories, and bla bla bla on top of my 80-hour week and this and that..."), but you're in the same boat so you just get over it and go home. Maybe you procrastinate or do actual work for an extra half-hour than you'd have done if the situation was different, but you don't "hide away". Ok, maybe you do it once in a while, but it's a bit like that nap you stole on a sunny Sunday afternoon: it doesn't feel quite right anyway - as your friend already experiences - and it's not something that should be a habit, as you wouldn't want your significant other to take that habit the other way around.
Quite likely, you want your significant other to occasionally do this:

Now, working from a home office is a slightly different situation, but it relates even more to the cause of your friend's problem: the noise. It's fairly difficuly already to work from home and take care of the kids at the same time if you don't have a caretaker and the kids don't go to nursery (for various reasons depending on country, culture, or what-have-you). If at all possible as you can imagine that handling 2 kids while working makes working a full shift a bit of challenge. But even when you are not taking care of them they do produce a, ahem, fair share of noise and distraction. And it's exhausting, like any noisy environment.
Kids are all different, and some are definitely noisier than others, but you can expect most of them to drain your energy rather quickly. Actually, it's not so much that they drain it, because if you don't actually do anything they'll still exhaust you. It's more that they drown your energy with theirs. You know, while they run around every where, scream, throw up, repeat a catch-phrase 100 times and do these other things they do.
So, back to my point... Now when I have to go back on-site, while I don't look forward to it, I surely do enjoy the trade-off and try to see the positive thing in both. When on-site, I enjoy the relative peace and quiet I get, and that I can focus more easily on work and I try to make the best of this time to get things done, even though that implies that the exhaustion comes from work instead of family over that period. And when I'm at home with the little monsters^Wones I appreciate that I can see them grow up and that before I always thought I was missing out on these things. I had to go back to work right after my first kid was born and worked long hours, and I'm sure every parent hates leaving in the morning before their kids wake up and coming back home after they've gone to bed. Sure, it's quiet, but there's something not quite right there either.
It's about seeing the glass half-full in both situations, and there's nothing wrong with that. As long as you're friend doesn't off-load his parental duties on someone else (too often) and loves his kids, then I don't think he's got to worry about anything. Being exhausted - physically, mentally and nervously - is perfectly normal, and longing for a time off is as well.
Schedule and Prioritize
Another suggestion could be to try to look back at his and his family's weekly routine and try to optimize it - without obsessing over it! - and see if they can grab 10 or 20 minutes here and there of "private" time, or if they can't get a friend or family to help.
I know that for more than 2 years we were far from family and didn't have many friends around and it was basically one of these times where you can't offload much (and nurseries were private and too expensive where we were, and so were caretakers), so it was pretty much just us. And it's hard. But once you have friends and family who can give a hand, don't feel ashamed to ask occasionally, and be sure to respect that help in making the best of the time they give you (by making it either productive or relaxing).
There are many "mistakes" we did as parents. They're more "rites of passage" than "mistakes", really, so just look at them this way. Off the top of my head, crazy stupid things we sometimes did included:
- Spending too much time doing chores (cooking, dishwashing, ironing...) that weren't absolutely necessary. Once in a while, a frozen meal is OK.
- Not planning in advance enough. If you pick up the kids from nursery and then you run around the clock to shop and cook and put them to bed, it's going to be tiresome. There are things you can prepare ahead of time. Food, for instance, can be prepared in batches.
- Not knowing when to ask for help.
- Not using time-outs effectively.
- Not going out to meet friends because we're afraid it's going to be too exhausting with the kids. Yes, it will be, but chit-chat and time with developed human beings is great for you.
- Not doing sports.
- Letting small things pile up. That bill you've got to pay, this thank-you note you need to write (I hereby sort of apologize for the dozens of people who never got theirs, but not really. I was swamped. Get over it.) or this door hinge you need to tighten.
The pattern in those is that they're all errors in prioritizing on the longer run.
Anyways, until you can work on fixing things, take a deep breath and:

Comic strips courtesy of Baby Blues.
"Keep Calm and Carry On" courtesy of the British Government, probably.