We're in similar situations, actually: I have a 7yo, 3yo, 2yo, and 10mo. Life is lovely, but chaotic most days, huh? I think the day-to-day can sometimes become overwhelming when you have so many that are so young, so it can be helpful to step back and examine what's REALLY bothering you.
Your kids are 6, 5, 2, and 1, right? So take the 2yo and the 1yo out of the eqution, because they're not school age anyway. Technically, the 5yo wouldn't necesarily be either since kindergarten is optional in most states. But focus on the 6 and 5yos. You said you're going to the library once a week or so. Are they able to pick out their own books? Do you spend time reading to them everyday? Do they have access to art supplies? Fun music to listen to? Do you go to the Farmer's Market? A Children's museum? The park? For nature walks? Do they have legos or blocks to build with? Fun video games to play or movies to watch?
I think starting a blog wouldn't be the best idea if you already feel you spend too much time on the computer. Plus, I think it shifts the focus to monitoring their learning, rather than facilitating it. Remember, your job isn't to TEACH them, but to support them in their desire to learn. So talk to them about their interests and make sure they have access to things that would enrich their passions and their environment. If they're interested in dinosaurs, check out some fun books from the library about dinosaurs or get a model dinosaur you could build together...but do it not with the purpose of making sure you can teach them about dinosaurs, but with the purpose of providing them opportunities to learn.
Talk to your wife and find out her specific concerns. "I'm concerned they're not learning" isn't really a specific enough concern for you to work with. "I'm worried that they aren't going to learn enough about math" at least gives you a direction to work with.
Another thing I find helpful to remember is that, because they're not in public school, there's no such thing as your child being BEHIND. The wonderful thing about unschooling is that it allows our kids to learn on their own timelines.
If her worry is more directed at YOU (if it seems you're spending too much time online, etc.) then that's something completely unrelated to unschooling that you can work on. Maybe don't turn the computer on until the kids are all asleep. I have a tenancy to be a bit of a twitter addict, so I limit it to times that I'm nursing the baby, and then work at staying present with the kids the rest of the time.
Anyway...I feel like I'm rambling a bit, so I'll end this now. If you're looking for a good book, Rue Kream has a great book that is an easy read, or I always suggest the website www.enjoylifeunschooling.com
Hope this helps some!
(Also...It's okay. This works. Your six year old is fine!)