Help! Our Dog is Driving Me Crazy!

I am at my wits end! My adorable canine friend is driving me insane. I love our family pet but enough with the "accidents" already. It's really getting old.

Our family has a really sweet miniature daschund. He is almost a year and a half old and is still having trouble grasping the concept of relieving himself outside. His name is Hershey, not because of the little "chocolate" kisses he leaves lying around, but because he has the most beautiful milk chocolate colored fur.

When we first got him just over a year ago we took him to "puppy potty training" class. We did everything we were taught and had him potty trained. He would even go to the door and ring a bell that I tied to a ribbon and hung down low enough that he could jingle it with his nose. We were all so proud of him that he actually learned this trick. Anyway, that lasted only a couple of months until he was about 6 months old. He hit "puppy puberty" according to our vet and was "marking" all over the house. She said we would have to potty train him all over again. Now, almost 9 months later, he still has accidents. My carpets are ruined and I'm at my wits end. It's disgusting!
I have 3 kids, and it grosses me out that they (and us parents) are constantly having to watch where we step. I don't know what to do! If anyone has any suggestions please, please, please share them. I would really appreciate it. I really don't want to get rid of the dog. We really do love him and would hate to see him go. But... I feel that we are failing at this game of potty training.

My husband thinks we should have him neutered and that would solve our problem. I'm not so sure. I had hoped to breed him in the future, so that idea doesn't sound so great to me. But if that's the problem than, we'll do what we gotta do.

Anyway, thanks for any advice you may have.