I agree, you should have the vet check Duke out just to eliminate a medical condition. Talk the behavior out with the vet and tell them exactly what has been happening. Especially since he snapped at Kay too when she touched him.

It is not uncommon for older dogs not to want anything to do with younger more playful pups. Especially if they are much bigger like Nala. Kiara is definitely a very high energy dog and Duke just may not want to be bothered. Simba is more his speed because Simba is also more layed back. Don't force the issue. They may never be "best friends" but they can learn to tolerate each other.

My two goldens before Dixie and Dusty were Taffey and Butch. Taffey was 7 when I brought Butch home. She really wasn't wild about him at all. First because she was use to being an only dog and second, he was all pup with lots of energy to spare! She would growl at him every time he came near. It was her way of saying "Hey kid, back off...I'm still the queen around here!" He didn't listen all the time and had to take his little punishment from her in the form of a snip or two. Never any blood drawn. It wasn't a fight, it was more of a warning. This is how dogs communicate. After she realized he wasn't going anywhere, she learned to "tolerate" him being around. When I wasn't watching, she would even be a little motherly to him!

After verifying Duke doesn't have any medical conditions that are causing him pain, if the dogs are together, don't expect them to be best of friends. Unless you have a full fledge fight on your hands, let them work it out. They will soon learn to "tolerate" each others company. The only disadvantage I see you having is because they are not together all the time. Each time they get together, it is possible they may need to establish the pecking order all over again. Realize this is normal dog behavior.

If your not comfortable letting them sort it out, then you will need to keep them separated by using leashes or not having them together at all. Just make sure to rule out any medical issues first though.