How much exercise is the puppy getting? I'm not talking a walk or anything, I am talking real running playing exercise? Puppies and young dogs for that matter need more exercise than we think. My sister has a 11 month old beagle puppy, who normally plays with my 13 month old Golden Retriever on a daily basis, I was on vacation last week with my puppy so there was no play date between the two. My sister said the difference between Reba was like night and day. She was a pill the first 2 days and then uncle brought his terrior over to play and for the next day she was well behaved but then the following day a pill again. It is because she was able to get lots of exercise and playtime that she was a good dog. Puppies need a minium of an hour of exercise. Playing tug, ball, fetch, with other dogs. Engaging exercise.
I agree with the crating thing, your puppy should be crated unless you are giving it your full attention. That way there is no chance he will make a mistake. Try taking him out more often, he is old enough to know to go outside, make sure you are recognizing his potty "signal". Hang in there, you are doing fine. I know when I first got my puppy I had one week where I felt like I was going to lose my mind, but luckly it only lasted a short time and after that it was easy going.
About your older dog. They will learn to tolerate each other. I bet if you get your puppy more exercise your older dog will come around faster. See if you can find some other puppies in your area to play with. Good luck.