Hello, my name is***** and I have over 20 years of experience as a veterinarian. I am sorry to hear about your pups eating some milk chocolate.
If both dogs were involved it may be difficult to be sure how many ounces each one ate.
A 10 pound pup would need to eat 2.4 ounces of milk chocolate to see symptoms of drooling, nausea, vomiting and diarrhea and almost 4.8 ounces of milk chocolate to see hyper-excitability and an elevated heart rate.
At higher amounts we can see muscle tremors and possible seizures.
So if one dog ate it all or most that would explain the vomiting. The good news though is if that dog ate most then perhaps the other one won't get sick. But if they split it then both are likely to have an upset stomach.
Since your one pup has already vomited it may be too late to induce vomiting. Has it already been 2 hours since they ate it? If so it is likely the chocolate is out of his stomach and it is probably too late to induce vomiting.
At that point you cannot change things much at home, all you can do is watch him for further symptoms now.
I would encourage you to get him to drink as much as possible and to get him out to urinate frequently. Chocolate toxins are metabolized out through the kidneys and can be reabsorbed from the bladder so we don't want them to sit in his bladder for long.
In most cases mild chocolate toxicity is out of their system in 24 to 48 hours. We generally begin to see symptoms, if they eat a toxic amount, within 4 to 6 hours.
It may help to with-hold food for the next 12 hours to stop intestinal spasms.
If he seems at all nauseous to try and settle either pup's stomach you can give either:
1) Pepcid ac (famotidine) at ¼ of a 10mg tablet per 5 to 10 pounds of body weight every 12 hours
2) Prilosec (omeprazole) at ¼ of a 10mg tablet per 5 to 10 pounds of body weight every 24 hours
These are acid reducers and should help him feel less nauseous. They are quite safe and can be used for several days if needed.
Then after a 12 hour food fast to decrease the symptoms of stomach upset you can feed them a bland diet for the next couple of days. A homemade bland diet is a mix of 1/3 boiled minced white skinless chicken or lean boiled hamburger and 2/3 boiled white rice mixed with some low salt chicken broth to make it easy to lap up and swallow. Feed small meals frequently.
If you do notice a very rapid heart rate (more than 160 beats per minute in a small dog) repetitive tremors or seizures then he should be seen by a veterinarian on an emergency basis for treatment. They can use injectable medications to control his heart rate and stop the seizures until the toxic levels fall.
Best of luck with your pups, let me know if you have any further questions.