First, I'm sorry you're having this problem Matopicus.
Second, I respect your rescuing the dog, and your honesty of how you tried to correct undesirable behavior and your accepting responsibility for said corrections. I agree that the techniques you used weren't the best.
Third, I'm no dog expert, but I have had dogs (1 at a time) for 31 years and have been able to train them to be pretty effortless and problem free. Current dog (see Avatar -- mostly siberian husky with a bit of shepherd I'm guessing, got her at age 1.5 years from Humane society, original owner didn't properly socialize her or train her to walk/etc., but otherwise a perfect dog).
I don't believe that certain breeds are more aggressive than others (with the caveat that some breeds are so inbred that they suffer from physical and/or physiological problems such as extreme nervousness, hip displasia, etc.). Some breeds to attract certain types of people tho, which I think is the main problem with pit bulls (tho I could be wrong -- I'd like to see good evidence that they've successfully been bred to be more aggressive, as there's a lot of bad evidence on both sides of this argument). I think 99.99% of the time it's the owner not the dog.
That said, for advice, I can only offer some general advice as not much info is available.
1-You have kids, they have to come first. If you can't be there all the time to supervise safe interactions, that's a big problem.
2-for the furniture chewing, I don't know the specifics so let me present a possible description that may give some things to try... I'm going to assume a typical morning -- dog wakes up when the family rises, dog is excited/hungry. Family is running around getting ready for work/school -- excitement and energy! Dog feeds on this excitement/energy, getting more excited/energetic. Maybe the dog is let out to do his thing in the backyard, then let back in and fed/watered, then family leaves dog alone at home. Dog is excited/energetic and bored. Nick's dog rule #1 -- a bored dog can be a destructive dog. Dog looks for entertainment and spies a couch! munch munch...
Possible solution -- in the morning, bicycle + leash + dog + run dog til tongue lolls out side of mouth for 15 minutes = relatively tired dog which is then left alone at home. Nick's dog rule #2 -- a tired dog is less likely to be destructive. It's not just being physically tired, but as Dog Whisperer says "birds fly, fish swim, dogs run." Running is psychologically refreshing/healthy for dogs.
This may not 'cure' the couch munching, but should help. If munching continues, kennel is next. Get dog used to kennel while you're home, at first for a few minutes with door open and with treats. Slowly increase, and hope.
Also, dogs feed off our 'energy'. I used to ask my first dog "want to go for a walk?" in an excited voice, I thought it was cute. Dog already was excited -- had energy, was looking forward to the walk, and I added to that. Now I am calm and quiet before walks, and have the dog lay quietly while I prepare. She's still excited but I'm helping minimize it and helping her control the excitement. Keeping your dog calm before you leave him at home alone can't hurt.
3-for the backyard digging, you need to catch them in the act, and the sooner the better -- as in 'nip it in the bud' as Barney Fife used to say -- don't wait til he's digging but stop him when he just starts to get the idea to dig. Yes this means you need to be there and watching during the training period. Also, tiring out the dog first helps, otherwise you're putting an energetic/excited dog out to find his own entertainment.
Some folks think any correction or other 'negative' training is abhorrent and criminal. I disagree. I think corrections can be humane and useful. Dog Whisperer talks about a dog's energy level -- on a scale from 1 to 10 assume 1 is bored dog falling asleep, and 10 is max excitement chasing-rabbit-just-out-of-reach excitement. To get a dog's attention you have to use an 'energy' a bit more energetic than the dog's energy level. For example, when I walk my dog (off leash) and she starts to head in the wrong direction I can barely whisper 'no' and she'll redirect to the right direction. However, when she spots a dead bird that's been sitting in the 116 degree desert sun for 2 days -- one of her favorite meals -- I have to practically shout 'NO!!' for her to hear me.
So, when you see your dog start to move towards the sprinklers just give a verbal correction, and best is when he first thinks of doing it, before he actually does do it. Experiment to see how 'energetic' it has to be for him to heed it. The earlier in his action the less energy needed. You may have to move to him and touch him (not hit/kick/etc., but touch as in a gentle nudge) to get his attention. Again, experiment on where/how to do this. For example, when training my current dog I found she responded to gently touching her ear. I'd prefer that she would have responded to a quiet 'no' but she didn't. Eventually she did, and I haven't ear-touched for 4 years.
Give rewards when dog is doing things you approve of, not just gentle corrections when doing what you don't want.
It would also help to give her some toys to play with in the back yard (bored energetic dog is destructive dog). Possibly some water toys -- shallow small plastic pool (tho be careful with your kids and pools and water)? A sprinkler that you occasionally run to help tire her out?
My dog digs in the backyard, but it's Phoenix AZ and hot a good part of the year, she does it to cool off, and we just accept that the back will look like no man's land.
With all 3 of my dogs I put in the effort to train them during the first couple of years, and was/am rewarded with many many years of pretty much effortless and joyful dog ownership. The effort is more than rewarded, both in time saved and in fun.
If you have any questions about the above or anything else, please to ask.
Good luck! 
