@sophie0813 I think its easy for anyone, especially men though, to get caught up in work. Work is predictable, uses standard language, and provides immediate gratification. Think about that, compared to being with young children...little kids are random and moody and require constant attention, whereas as work you can say "I'm going to work on this for an hour" and then go do that. When you make your kids lunch, they complain, ask to have their hands wiped, then run off to play leaving the table a mess. When you finish a work project, your boss says "Great thanks!" and then you can turn to the next thing. With your kids, you are basically doing whatever you can with the hope that in 25 years when they have their own kids they are good people, at your job you get a paycheck every 2 weeks.
The other piece, and this may be a cultural or family thing, is that when a couple decides one partner will be a stay at home and the other will work, and especially when it is a man going to work, there may be some expectation that he is the breadwinner, you raise the kids/run the household, and may the two lines never cross. This may be furthered by his own experiences - if his mother was a stay at home, his memories of what she did aren't from when he was 3, they are from when he was a teenager. If all your kids were teenagers, yes, you would probably spend more time managing the house and less with kids attached to you.
So... that's my "why does it seem like my husband is desperate to get back to his job" perspective, but what to do about it? My take is that he needs to be forced to engage. I feel like I didn't really 'bond' with my kids until I was forced to be a stay at home parent. Yeah, the first day or so sucked, but once I realized I was in it, I started developing ways to solve it (I mean, its exactly what you've done, right?). Once I got comfortable with things like going outside with the kids, I realized its not so bad and can be really fun. Now, when my wife has to work on the weekends, I just pack my kids up and go somewhere.
I also personally don't really enjoy taking my kids to the zoo right now - they are too young and its waaaayyyyyy to stressful - but that doesn't mean there aren't plenty of other things that are tons of fun. I really like going for walks in the woods - its easy, the kids seem to have fun, and they seem pretty tired when we get home.
I'm a big fan of the sink or swim approach, but if you think that is just going to be a disaster, what about trying something with one of the kids? I wonder if giving your husband the 4 year old for a couple hours on the weekend would be a way for him to get some more time and also give you at least one less to be responsible for. Or, alternatively, you go somewhere with the 4 year old and leave the other two with him.