Did you do any research before getting a bunny? Digging and chewing are natural and normal behaviors for bunnies. No amount of training is going to make those behaviors ‘go away’…it is just what a bunny does. They are nothing like cats or dogs.
Create a dig box for your bunny. I took a large, low sided cardboard box and filled it with shredded paper. Underneath all the shredded paper I placed a few treats, some hay and some pellets….just a bit of each. When my bun is out of his xpen enclosure for play time, he loves to go to the dig box and dig, dig, dig and find his surprises!
Chewing carpet is a behavior that is normal as well as much as it is unacceptable. Not only does it damage your floors, it also is harmful to bunny if eaten. All outside play time in the room MUST BE SUPERVISED. Period. No exceptions. If he tries to chew carpet, clap your hands loudly and say NO! in a firm voice. If that doesn’t work, then simply place him back in his enclosure and playtime is over for a bit. It isn’t an instant fix and it will take him a while to get it but he will eventually come to understand that if he chews carpet, his playtime outside his enclosure is over.
Everyone will tell you that neutering is absolutely necessary…and they are correct. What I will tell you is that it is not an instant fix either. Young bunnies must be watched extremely closely just as you would watch your young children closely. You will still have to teach your bunny what behaviors are appropriate and what behaviors are not. Bunnies are not an ‘easy’ pet…they are just as much work as a dog or cat…maybe even more so due to their very sensitive digestive systems.
Good luck. Take some time to do some reading on this behavior forum. It will help you understand bunny behavior. Check out the House Rabbit Society page as well.
**Do you have cardboard boxes for your bunny to play with? I took larger boxes and cut doorways in them for our bun to run through while he is out playing. Of course instead he jumps on top of them and destroys them by tearing the layers of cardboard up! Great fun for him and not exactly how I thought he would use them but hey…they are his to play with as he chooses. Bunnies like to dig, chew, rip and tear things up…so give him appropriate things so he can do his natural behaviors. I have heard of other members giving buns phone books to destroy and dig. Its going to make a huge mess but again, that is pretty typical with bunnies. You mentioned that you have to clean their enclosures every 2-3 days?!!? Geesh, I clean my buns every single day and I don’t think its much of a big deal…but I knew what to expect. And yes I work full time and have 2 children as well