The first problem is probably boredom, our dog is well behaved, but if he thinks you are ignoring him he will purposely do something he knows he isn't allowed to do. Take her for a longer walk before you leave her alone, take along toys that she can play with so she is being stimulated and to make her more tired, things you can throw are good, that way she will be doing a lot of running around. You could use a small selection of toys to do this, and use them to play with her inside the house, then leave these toys with her when you go out, so she associates them with playing. Then she has something to do when she is alone.
Walking will sort out her nails as well, if you take her to a park, don't drive there, walk, her claws on the path will cause them to wear down, it isn't as fast as clipping, but it works really well, our dog gets his nails clipped when he has a hair cut, but truthfully, he doesn't need it doing at all, it just makes them really sharp!