Puppy and older dog questions

I hope this is the right place to post this.
We’ve had Archie since 8 weeks old and he is 16 weeks now. His bite play and mouthing us is under control unless he is over excited and he forgets. But will listen as soon as you correct him. Buddy is our 11 year old bichon. He loves every dog he meets and is very respectful if the other dog doesn’t want to interact. The two have been living under the same roof for two weeks now. Buddy was staying with my parents because our new house didn’t have a fence. During this time I would take Archie to buddy to have a play a couple of times a week. Archie would jump on Buddy and nip him. He was somewhat tolerating this but now that they are living in the same house Buddy growls and snaps almost every time Archie comes near. Archie doesn’t give up. To make things worse, 5 days ago Buddy had an emergency surgery to remove a lump that he has had for a year that now got infected. I try and get them close to each other without Archie jumping on him, but Archie gets so excited and starts nipping the second he gets to Buddy. I have to give Buddy some time to recover. So if Buddy is outside which is most of the day, because he loves being outside, Archie is free to run around in the house. At night buddy sleeps in the house and Archie is in his crate that has a playpen attached to it. My question is do I correct Archie or do I let Buddy be the one to discipline Archie? Do I correct Buddy if I feel he is over correcting? The way I imagined it was them being friends from day one. I knew Archie was going to do what puppies do but Buddy surprised me with how intolerant he is with Archie. Could it be that Buddy’s health is not a100%? Or am I overthinking and all of this is normal? I’ve never had a senior dog and a puppy at the same time.
Sorry if this post is too long and confusing
Thanks for reading

I can only share my experience with mine.
Nifty was 18 months old when we all went to fetch Opium.
Nifty is a quiet couch staffy who loves everyone.
Opium is a hyper staffy who rarely sits still.

Opium loves to play with Nifty and especially grabs her by her ears.
Nifty would tolerate this when Opium had just come home but at 9 months old now, Nifty is certainly getting much less tolerant.
I do tell Opium not to grab Nifty’s ears and I always keep an eye on the girls when they play/argue.

I know young puppies have a certain smell and any well balanced adult dog won’t attack a baby.
However, when they grow up a bit and lose this baby smell, then adults might try to teach manners to an over exuberant youngster.

If Buddy is already growling at Archie, I’d be guessing that he’s warning him to back off.
I would let Buddy express himself and see what happens.
Maybe you can try to distract Archie from throwing himself on Buddy by inviting them to play with a toy together, for example.
Certainly watch them and their body language. Then you can call timeout before the situation gets out of hand.

Buddy being a lot old will tolerate Archie's puppy manners for so long but will certainly put him in his place when he oversteps the mark. Archie will soon learn how far he can go! Katy is very good with pups but when she's had enough she will growl, then bark but if they're not heeding the warning she will snap at them but not touch them.
Just keep an eye on them & if you feel Buddy has had enough take Archie away so he gets some peace

Thank you so much for the replies and advice.
Archie sounds like your Opium. Very playful.
When Buddy snaps it’s definitely just a warning. He definitely doesn’t touch him. And then he just walks off and ignores him. Archie looooves anything furry and fluffy. He always goes for my ugg boots, the kids stuffed toys. And buddy having a woolly coat doesn’t help . Their interactions are always supervised. Definitely don’t want to keep them apart all the time as I feel they need to be around each other.
Thanks again. I’ll keep you updated

Archie&Jess wrote:
When Buddy snaps it’s definitely just a warning. He definitely doesn’t touch him. And then he just walks off and ignores him.

Just make sure that when Buddy walks away, Archie isn't allowed to follow him. That should keep the peace a little easier!

gillybrent wrote:

Just make sure that when Buddy walks away, Archie isn't allowed to follow him. That should keep the peace a little easier!

Sorry I didn’t reply earlier. Somehow I missed this

That’s interesting. Why not? Does that teach Archie that when buddy walks away he is doing something that he shouldn’t? Similar to something we would do when he was biting us. That makes sense. How long do I then keep him from approaching buddy again? Because Archie wants to play with him all the time

I would have thought that it would be to enforce Buddy’s message of “that’s not acceptable, leave me alone”. If Archie follows, Buddy will probably snap again but that could lead to more (fight) which Buddy doesn’t need for now.

If you are supervising them whilst they are together at the moment, you could for example give Archie a toy to play with, so he turns his attention away from Buddy and doesn’t follow him.

Got it. Thank you so much.
For now any time they are together I’m with them all the time. Buddy seems to be feeling better and healing well. He wants to smell Archie and goes near him in the last couple of days.  There have been a couple of licks as well.
I’ll keep you posted.
Thanks again.

Glad to hear that Buddy is well on the road to a full recovery and that your boys are getting on better.