Could be a dominance thing, or an attention thing, or an excitement/stress because there is a new dog thing. Is he peeing where the puppy pees? Clean where they pee w/ vinegar and water. Oxyclean is now making a pet stain cleaner that also neutralizer the odor pretty effectively, or so I've been told. If it smells like pee, they'll be repeat offenders! and their nose is much better than yours. Correct the older dog as you did when he was a puppy, which hopefully involves taking him outside, and does NOT involve rubbing his nose in it. You may need to confine him until they get used to each other, should only take a few days. Make sure the older dog is getting plenty of attention, too. Best of luck and congrats on the new puppy
Which one peed, older or younger? House training can be very frustrating. Your certainly not the first one to have that happen, although I doubt hearing that helps! The younger dog is really to young to understand what is expected of him yet, so it is up to you to figure out when he is going to go, and get him out there. When you take him out of the crate, or when he wakes up, or has a big drink are likely times. Take him to the same place to pee each time, the smell will help him to figure out why he is there. be sure to give him enough time to poop, too. Do you have a yard? Setting a puppy play pen up outside the back door can be a real life saver when your patience runs thin. You can just put him in there, and watch out the window until he goes. If you can get one big enough to hold both dogs, you could put them out there together, and the older dog can do all the peeing/marking he feels the need to do to establish dominance over the younger one or just get to know the younger one and get over his excitement (whatever his issue is that's got him peeing in the house again). Probably a good idea to keep an eye on them while this is going on, although I doubt a 10 month old and a 2 month old would do each other any harm. If you read some of the other house training threads, you'll find other good tips. Try not to lose patience with them. At this age, the most important thing is to establish a good relationship with the dog. How you handle things now can affect the younger dogs character permanently. He is in a fear stage at 8 weeks old. Are you familiar with what that is? Lots of info. available online if you do a search. I'd fill you in, but it is bedtime. Good Luck!