You've had some good advice here. I will say that I think you better hold off on an overnighter for the 10 day old for a while. That's a time when everyone needs creature comforts.
That said, I'd have to ask yours and your wife's age. If you were say early twenties when the older ones were born you're probably pretty tough now. If you were in your thirties then lets rethink this. So many people wait until they are in their mid to late thirties to have kids these days, for many valid reasons, but most of those people are a bunch of wussies with mamby pamby children who whine at each other nonstop. Parents seem to read too many parenting books these days instead of just going with the flow. Kids don't come with instruction manuals. They're not a TV so don't try to operate by the manual. I was 23 when my first child was born, 29 for the last. He was born with a lot of very serious health issues. When he was three weeks old, 12 days out of NNICU, we took them all to the mountains for Easter for the day. We hunted eggs in the snow. We had no clue what was right or wrong but we had a blast. Never knew if we were doing it by the book or the right way. We just had fun. They all survived quite nicely and are productive young adults.
So back to camping. Roy gave you great advice. Make it short, try to make it comfortable, and most important, make it about the kids. Don't go out there thinking you're gonna go scouting for "the big one" while your wife sits in a tent. Uh uh. You need to be the chief cook, bottle washer, fire builder, kid washer. Make it fun for them and it will be fun for you. Believe me it will be something you look back on happily if you keep it fun.
I also agree with Roy on taking them individually or in small age coordinated groups. My older son and I started a special boys-only fishing/camping trip tradition when he was very young and those are some of the best memories I have. I didn't catch the most or biggest fish and I was frustrated many times but I wouldn't trade it. I did the same thing with my younger son a time or two despite certain limitations and we had a blast. My older son and daughter and I went on her first deer hunt for a couple nights when she about 12 and he was 10. Just the three of us. We laughed, told stories, played charades, ate crappy food and generally had the kind of time she still talks about even though she no longer hunts. Didn't kill a deer but it was a fantastic time.
By the way, my kids never had a chance. My wife was in early labor when we were deer hunting one year, and I'm pretty sure both of my sons were conceived on camping trips to my favorite hunting mountains, by design I might add. Made them tough.
I hope I didn't offend anyone, but if I did, oh well, I'm older and I don't really care.
