You got some good advise & your son has a point..... Taking a dog to a shelter unless it's agressive is the lazy way out.....but I know you're frustrated.
It sure does sound like you need to start from the beginning and try to re-train them - or FIND SOMEONE WHO CAN - there are many people looking for yorkies that would be able to invest the time to train....with all the accidents you can't be enjoying them too much and that's just a shame for them and you.
PLEASE READ THIS ABOUT Taking a dog to the Shelter....I think it may change your mind on them
http://www.yorkietalk.com/forums/sho...d.php?t=54913I
I wish you all the best