from watching my nieces and nephews growing up and watching lot of those nanny shows, i think the key to your children respecting your word is follow through, if you threaten them and nothing comes of it, they soon realise the is no weight to the words.
you dont need to shout (but children can make us so frustrated) you need to make them understand that if you say they will be punished, then they will be punished.
I know that trying to set a new standard in your home is going to be a very turbulent time and the kids will try push the boundaries as far as they can. But u must stay strong, and don't forget to reward good behavior with time and affection.
Just my thoughts on what i have noticed/done while babysitting, i am certainly no expert but maybe give it a try?