my undersocialized dog

Question
First a little about our dog, he is a black lab/ walker coonhound mix. We got him about a year ago from an ad we had seen. We were told he was skittish around new people and he was housebroken, good with other animals and children. We have 3 children ages 12,9 and 6. When we met him we took the kids with us to see how he would do. He was real skittish at first but after we were there for about 15 mins. or so he started coming around us. So long story short, we ended up getting him. He is good with my kids but other kids that come around he is not. He has nipped at a couple neighborhood kids and my niece. He is not good with other animals, he has tried to attack my moms dog and another dog in the neighborhood. He is always digging in the trash can and chewing up trash, toys, etc. He sometimes whines when he has to go out, sometimes he doesn't whine and uses the restroom in the house. If anyone knocks on the door he jumps up on the door barking and going crazy. You can't open the door without having to fight him back or putting him in the cage first. He used to be real bad about running out of the door anytime you open but that has gotten a little better, not much. We have tried dog training but I had to stop going because it was too much money and he only listened to the trainer. When we would do the exercises at home he never listened to me. I am at my wits end and don't know what to do. I guess my question is there anything that I can do myself without having to pay money for a trainer? Or how can I make him better around other people so I can take him to the vet when he needs to go or the groomers because he needs his nails clipped now and when we took him to get his shots and neutered that was a nightmare. I don't want to give up on him, he can be a really good boy when he wants to, and he love to cuddle. Also, I don't know really how old he is, we were told he was about a year old when we got him and that was last Jan. so I am guessing he is 2 yrs. old. If you have any advice or tips I would greatly appreciate it.

Answer
It sounds like you've got a frightened dog that simply wants someone to take charge and direct him as to how he should behave.I'd suggest you find a dog trainer who will allow you to simply sit in their class and observe. Also, I'd suggest you do some intense reading on dog training. You could start with some of the many articles on my website at www.perfectdogtraining.com. The solution to your dilemma does not involve training the dog. The ultimate solution is to somehow get you trained.