What to do with misbehaving pets?

Hello. I own two Miniature Pinchers and have had them for quite some time, but they are becoming very unreasonable to deal with. They use the bathroom in the house, and my family has to board them -- which is extremely costly -- whenever we go anywhere. I realize that this is our mistake, but the situation has become impossible and we need a solution. I just called a shelter, but they said that they wouldn't accept them because of their aggressive behaviors. Can anyone offer a solution? I really do not want them to be killed at a shelter. Please help.