You have a serious situation on your hands if your Dalmatian has bitten or tried to bite you, a family member or someone else. First of all, you cannot put this dog in a new home. Period. The reason is that you would be at risk of being sued if this dog bites someone in the new family and you have a moral and legal responsibility to protect the public from an aggressive dog.
The first step is to try to find out why the dog bit in the first place. Your dog needs to have a thorough physical exam to find out if there is a medical condition that caused the aggression. A dog in pain from arthritis, bladder stones, ear infections, etc. can bite. Conditions such as hypothyroidism can also lead to aggressive behavior. A blood test can provide your vet with a lot of information about your dog's health. If a medical problem is discovered and treated, your dog may be just fine.
If there doesn't seem to be any medical condition that caused the aggression, your next step would be to contact a canine behavioral specialist to see if there is a way to prevent any more aggression through behavior modification. You can find a dog trainer through the Association of Pet Dog Trainers.
Here are some links to aggression articles that might also be helpful:
If there is no medical problem and the aggressive behavior cannot be modified, or you don't want to keep the dog regardless, your only choice is to take the dog to your own veterinarian and have it gently put to sleep while you hold it in your arms. Please don't take your dog to a shelter to be put to sleep. The dog will be terrified until they finally have time to euthanize it or the shelter might accidently adopt the dog out to someone.
This is a very sad situation for all involved but if the problem can't be fixed, it is better for the dog to be humanely put to sleep than to risk someone being badly injured or even killed.