First of all, puppysitting is a PITA. Seriously. It's easier if the puppy is yours and you get the satisfaction of knowing it will one day be a dignified adult, but if it's not yours and you're just focused on getting through two weeks, it's not mucy fun. So I sympathize with you.
Here's how I get through it:
1. Keep the puppy on leash tied to you at all times. You may have to soak the leash in Bitter Apple or something to make it taste bad if he chews it, or you may have to use a chain leash to protect your leash. The only time he can be not on leash is if you're in a closed room with the cat out of the room, or in a securely fenced yard with no chance of a cat coming in.
2. Always have a toy in your back pocket. If he starts chewing on something he's not supposed to, shove the toy in his mouth and PRAISE him for chewing on the toy. If he picks up a toy on his own to chew on, PRAISE that too and play with the toy with him. If you give him the toy in your back pocket, do not forget to replace it very quickly, as he will probably get bored relatively soon.
3. If he starts digging on the rug, growling at the cat, or doing anything else that's not appropriate, get his attention off that behavior and refocus him onto a more appropriate behavior - such as playing with the toy in your back pocket.
4. Have a variety of "pacifier toys" handy - frozen kongs, knucklebones, etc. - for when the toy in your back pocket is no longer fun.
5. Don't be afraid to use the crate. A well exercised puppy should sleep about 18 hours a day. But they don't know that.... they usually won't just go off and go to sleep on their own. When they get particularly grouchy and annoying is usually when they are particularly tired and need a nap, so put him in the crate and let him nap for 1-2 hours.
6. Don't use the food bowl.... feed all meals in food dispensing toys. These not only keep him busy for a few minutes - giving you a few minutes of peace - but they help to tire him out mentally. You can put the food in empty plastic bottles which he has to knock around to get all the food out; put the food in a cardboard box that he has to tear up to get the food out of (best to do this in the crate); or use any number of food dispensing toys that most pet stores have. At this age, you should be feeding him 2-3 times a day, so that should keep him busy for a good long time.
