There are many members who have had the same issues you are dealing with right now, and I’m sure there will be more posted tips to help you.

The destructive behavior:  That should get better after the hormones die down (can take up to six weeks) and as she ages, but young bunnies (under 2 years) can really  be energenic and need things to keep them busy to prevent destruction. 

The digging box is a good idea.  Stay away from corncob as that can cause impaction in a bunny’s digestive tract.   Instead, crumple up paper in a loose little balls, (golf ball size, and use shredded paper if you have a shredder. Some bunnies like to also push, and rearrange blankets, so if you have an old toss blanket, you can try that too.  (if your bunny starts eating it, then take it away)

Place phone books in the area your bunny likes to chew and/or place a phone book in the path of your bunny – just partly blocking one of her regular routes – like behind the couch  or ?? 

Also, it might be a good idea to just use a plain old cardboard box first before purchasing a kitty dome.  She may not be interested in a digging box, and so you haven’t wasted any $$. .   Also, when you do create an enclosed dig box or hiding place make two holes – many rabbits prefer to have two escape routes, otherwise they won’t stay long.

Bunnies dig for many reasons – Regarding Carpet:  1. Boredom (but that’s not always the case!)  2. To try and make a sunken lounge area.   3.  A smell from food, a particular cleaner, a previous pet (even though it’s not detectable by us)    Either way, chewing carpet is never acceptable, so I keep a squirt water bottle near by so I can shoot a harmless stream of water to chase the bunny away.  If a bunny does it again, then s/he should be put back in her pen.   It will take time for her to understand, but it doesn’t take tooo long for them to associate carpet chewing with lack of freedom.

Regarding diggin at your lap, again could be several reasons.    1.  Move!   2. Put me down!  3. Pet me!   If it hurts when  your bunny does this, give out a little high pitched squeel as this is how they communicate to each other regarding pain.   This should make her stop, unless she wants down, and doesn’t care if it hurts you.

Regarding how to catch her.  For now, you may have to catch her with the towel method, but even with that, once you have caught her place her just before then entrance of her cage, and block off escape, so that she will go in on her own.  THEN, give her a treat for entering.  As she is going into the cage and while you are giving the treat, repeat the a key word like "home" so she begins to associate going into her cage with that word.   Depending on the bunny, it can take a few days or a few months. (Don’t use the key word when  you are trying to catch her with the towel – of course)

My bunnies know  words like litterbox, get home and treat very well.  You can even start with teaching your bunny the word treat – as they learn this one VERY quickly.   This way, you can actually entice your bunny to the location you want with that word, and then teach him a new word with a new assocation  – like home, and litterbox etc.  

It’s easy to teach a bunny "Treat!".  Many people say their bunny comes running at the sound of opening a package.   If yours already does this, then you just say the word, with the sound, and then just eliminate the sound.    Otherwise, you just say the word treat exactly at the moment you give the treat to your bunny.   So that you don’t overload your bunny with treats, which can be immediately very harmful for him, just cut the treat up into tiny little itsy bitsy pieces.   Do training sessions like this everyday.