How do I deal with my 13 month old's whining and defiance?

I love my son very, very dearly, but he's about to make me crazy. His daycare says he's an amazing kid who rarely causes any fuss and plays really happily, but he couldn't be more different at home (especially when Mommy is in the room). Sometimes he'll whine literally all day when he's awake and giving him milk/feeding him/playing with him only works for a couple minutes at a time. I can't cook or clean anything with him around sometimes because I have to constantly keep him entertained to prevent the whining (and I'm an extremely attentive Mommy). Ignoring him makes it worse. He is also into EVERYTHING, especially things I don't want him to have. He's attracted like a moth to a light to our kitchen trash can and I am endlessly telling him not to touch it. Yesterday, he looked at me while I was telling him no and said "NO!" Then, he smiled and touched it anyways. There are so many little things in the house that I'm constantly pulling him out of (toilet paper, the cat food, Daddy's DVD collection, various books he likes to chew on, the lamp he likes to jiggle, electrical sockets that he pulls the child proof covers off of). Anyhow, how do you ert yourself with a 13 month old? I feel like I am fighting a losing battle.