Hi XXXXXXXXX~
It could absolutely be anxiety that is causing the drooling...however, if he ate his dinner, that's a good sign, and the fact that he ate it with the other dog right there is an even better sign.
Just like humans who lose someone, dogs do take a little time to grieve over the loss of a pack member, and adding in a new dog could have made that process a bit more confusing...however, I don't think you should rush to get rid of the new dog just yet.
Adjusting could take a little time...but there are products that can help with the anxiety while that adjustment happens:
A couple things you could try would be:
Melantonin is an over-the-counter drug that can be used to treat some anxiety issues in dogs. The dose you would give would be up to 3 mg given orally whenever necessary up to every 8 hours. More information can be found here: http://www.petplace.com/drug-library/melatonin-melatonex/page1.aspx , which includes risks, warning signs to watch out for and other bits of useful information.
Try a DAP collar. These are collars that are impregnated with a man-made version of the dog appeasing pheromone, which is a pheromone that nursing bitches give off to their pups to help them feel calm and secure. It's something that humans can't smell, but it has an amazing effect on dogs with anxiety and other issues. Although you can find them at your vet's office..you can also find them online at places like Amazon.com and Ebay for much cheaper. Just make sure they're DAP brand, as they seem to work better than some other versions.
When I deal with anxious dogs, I use the collar first, then add in the Melatonin if needed.
I'd give it a good week before I made any decision about getting rid of the new dog. I suspect that your dog will warm up to the new comer in a few days and things will get back to normal.
I hope this helps.
Certified Veterinary Technician
Associates Degree in Veterinary Technology. State and Nationally certified.