Your male, Diego, considers the house his and that he is the alpha male. The other two dogs are visitors and likely it is your sister that pays attention to them. With the puppy, you are showing it a lot of attention and even elevating it to a position highe than the male by putting it on your lap. Puppies know little about acceptable behavior around adult dogs that are not their mother, so once they go to new homes, the resident dogs teach them. They do this by reprimanding them for unacceptable behavior. They usually start by growling at them to show the behavior is unacceptable. If that is ignored, they will move toward lunging at them and trying to nip them. If the pup continues to display behavior the alpha dog feels is unacceptable, then he will have to make the reprimands more physical until the pup learns to behave. Once in a while you will have a little injury but for the most part, there is a lot of snarling biting (no actual injuries or minor injury) and squealing. This is relatively normal behavior.
Behavior that an alpha male might find is unacceptable would include pushing past the alpha dog to get attention first, eating from the alpha's bowl, eating first, grabbing treats or playing with the alpha's toy and all toys are the alphas. So you may have inadvertently be contributing to the problem by showing the pup a lot of attention. So you can help the situation by encouraging the pup to obey the "adult" rules. Additionally, you can show your male attention first and feed him first and be sure he gets out the door before the puppy does.
I also recommend obedience training for your male and puppy. This will teach your male that you are the ultimate boss of the household and it is your place to give the reprimands. Of course, you will need to reprimand the pup when she gets in the alpha dog's space or displays other unwanted behavior including aggravating the older male.
The following site is helpful for teaching you how to train your 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.
Training works best if you train at least 30 minutes a day (two 15 minute sessions). I would start making your dog work via the Nothing in life is free program (NILF). It is outlined below.
You can also keep a leash attached to the male and puppy all the time, even if they are short leashes. Then keep an eye on them and use the leashes to issue reprimands in the form of a short tug and firm "NO". You can encourage the behavior you want by giving special treats like hot dog or liver slivers as well.
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