Hi! I can help you with your question.
I am sorry to hear about the situation with your dog. That is a very tough position to be in. One, the dog is costing you more than you can afford and two, the children are emotionally attached to the dog.
One of the things you can try is to find a local Humane Society clinic. They offer low cost visits and shots. You can explain your situation and see if they can help. They work with anyone to help to find the best solution. http://www.humanesociety.org/
Another option is if someone close to you could take the dog. That way, the kids could still see him but you would not have to care for him.
You can also buy a cheap flea collar at Walmart instead of having a vet treat him.
If you cannot afford a visit to the vet now, take time to save for it. As long as your dog is up on his shots, he should be ok.
Whatever you decide, be sure to include the children, even if it is just talking to them about their feelings. Children can deal with changes or loss, but they fair much worse if they cannot share how they feel.
About your son's teacher, there is nothing wrong with you moving him to another school. It sounds like this teacher is a bully and she is using her position to emotionally abuse the students. If the school is not listening to parents concerns, then the next best option is to take action by removing your son. It is better for him in the long run. Trying to learn in that kind of environment is nearly impossible.
It is great that you are learning more about your situation through the support groups and books. With any difficult situation, the more you know the better your resources in helping yourself and your children. If I can help provide any more resources, let me know.
Please let me know if you have any further questions. I'm happy to help.