I do want to thank you for supplying so much helpful information.
Prior to the new dog, your Papillon was likely the alpha by default. When a dog is a puppy and raised with an adult, the adult is usually seen as the alpha dog. Thus there is no dominance fighting between those two dogs.
However, when the spaniel was added, she was maturing into an adult female and after a short while would attempt to move up in the pack rank. The higher you are, the more privileges you get theoretically. In a pack situation, the top dog gets to eat food and decide when others do, they get to pick what toys they want to play with or take from another. They are supposed to be respected by the other dogs and other dogs are not allowed to push the top dog out of the way. Now I should warn you that some people do not believe that dogs act in a pack manner. Owning a large number of dogs and working as a behaviorist and trainer for 18+ years has shown me that there are leaders and followers in a group of dogs. While it may not be as intense as it s in a wolf pack, it still exists.
Now the spaniel was the boss in his house and she came to your house and wasn't the boss and wasn't treated like the boss. So she likely challenged the 4 year old. Often the challenge can be just eating first or pushing the papillon out of the way. She would not likely just submit and give up her position without a fight whether it was a growl or a nip. If the spaniel was dominant which it sounds like she is, she would fight back to gain that top dog position. Now the older dog might not understand fully what was going on and likely you still treated her as the alpha dog by giving her attention and feeding her first. Even though you did these things, the new alpha dog would expect her to not accept them since she wasn't the boss anymore so she would reprimand the papillon which is what seems to be occurring.
The lab would support the new "top dog" and help reprimand the older dog. It is bad but what ends up happening. Springer spaniels can have problems with sudden aggression anyway and often it is believed that a thyroid condition may contribute to that issue, so you might have a thyroid panel done on the spaniel.
To correct the situation, you have to gain total control over all the dogs. I'd start with the spaniel and lab. I'd also suggest basket muzzles for both of them to prevent any additional attacks on the papillon. They have to be basket muzzles so they can still breathe normally and eat and drink. Now you can't keep muzzles on them all the time, so be sure you have a crate that you can put the papillon on spaniel in alternatively so the dogs don't have to wear muzzles all the time. I do not suggest separating them for any length of time unless the separation will be permanent because each will feel the area they are in all the time is theirs and will attack the other if they enter that area.
The following site is helpful in helping owners train their dog. Be sure and click on the link to the page on obedience at the bottom. and links on subsequent pages leading to detailed instructions.
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Additional training can also help. all dogs should be leashed and if one dog even looks at the other dog, a correction should be done. Any sign of aggression including a prolonged look, hair raised on the shoulders, a growl or even a stiff legged walk, should be corrected. A correction is a quick tug of the leash and a firm low toned "NO". Once you have done this couple of times, you should notice the dogs ignoring each other. When that happens, you will want to reward them for the desired behavior. Again, use tasty treats like the hot dog slices. This teaches the dogs that you WILL not tolerate fighting in YOUR pack.
Start with the spaniel and the papillon and keep the muzzle on the spaniel. I'd keep it on during training sessions until you are fairly confident the situation is under control again via the obedience training and this training. Sometimes adding another female to the mix can never be resolved and you end up keeping them separate. In my opinion, females are much worse than males in this regard. You can read about this issue here:
If this was me, I'd try the training first but start thinking about rehoming if you can not get them under control.
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