Our Chihuahua-Poodle has bitten everyone in the house. How much would it cost to shave the dog's teeth of?

I live with my sister who has a three year old mix breed (half long haired Chihuahua, half Poodle). He weighs about 12 pounds and has been fixed. Anyway, he's always been fairly protective and aggressive, but in the last year or so he has become progressively worse. My sister and her boyfriend are the only ones that are spared his biting. He's drawn blood on me half a dozen times and has done the same to others. It used to be that he only bit me when I tried to touch or pet him while he was on or near my sister. More recently, however, he tried biting me when I was rubbing his belly. He usually loves having his belly rubbed and always rolls right over for me to do it. He also tried to bite my sister's boyfriend for the first time recently. Is there anything we can do to get him to stop? I recently saw something on the Animal Channel that said that once a dog bites hard enough to draw blood, it is too late to get them to stop. It then went on to talk about a procedure where a vet shaves off the sharp parts of a dogs teeth so that they only pinch rather than break the skin when they go for a bite; psychologically the dog knows it can do no harm so it stops biting. Anyway, is this a good idea to look into? If so, how much does it usually cost and if not, what other options are there?

Thank you,
Ian