Cat Is Misbehaving! PLEASE HELP!!!!?

My husband and I had four animals. Two cats, one is 6 yrs and the other just turned 1yr. And two dogs one is 8yr and the other 1yr. Our cat that is 1yr old is always into everything. Boxes, bags, plants, etc... He is very curious and playful. That is how he earned his name demon because he truly is one. Well last week my neighbors found a chihuahua puppy in a store parking lot dumpster. They brought it home but it is scared to death of their 3yr child. So they brought it to us. (before anyone jumps to conclusions about having 5 pets I live on 5 acres and have no children so our animals are well taken care of and have plenty of room to run except the cats live indoors only due to coyotes) Anyways since bringing the puppy into our home our 1yr cat has been worse than ever and I think it might be because of the puppy but the cat has lived with 2 HUGE dogs that chase and play with him everyday and this puppy doesn't even weigh 2lbs. And when I say he is worst than ever I mean really bad! He has started tearing a huge hole in the cat food and dog food bags so they spill out on the floor. He has literally tore up every toilet paper and paper towel rolls in the house due to him getting into bathroom and kitchen cabinets, and with his new found skill of opening cabinets I woke up this morning to all my dry goods out of the cabinet and shredded on the floor (I mean every single one that he could possibely shredded was in little bity pieces). Worst of all he is breaking my blinds in my windows. I have now replaced 6 blinds for the low low cost of 120 dollars. The weird part of it all is that he goes around howling and he is fixed. I love him to death but he is driving me nuts and I fear that he might get worse and tear up my furniture or worse yet start peeing on things. If that happens I will have to get rid of him and I don't think I could bear to do that because he it "my" cat. I have brought up the idea to my husband that we rehome the puppy but we took the puppy to my moms house for a night and even with it gone for 24 hours he still continued to destroy my house. He is so loving but I don't know what is causing his behavior or what I can do to help him. He hasn't lost attention that he normally gets and he still follows me everywhere. Also every morning him and I play before I even get out of bed. The puppy is caged at night like the other dogs in a spare bedroom and the cat still sleeps next to me. The puppy doesn't torment him by any means. I think the puppy is scared of the cat seeing he is 10lbs bigger than it and avoids it at all cost. Has anyone dealt with a problem like this??? Please I am desperate for help I lost over 30 dollars in food from my cabinets and I installed child locks on them for a cat!