Wow!. I own a chihuahua. Another day, another bite.
Unfortunately, because small dogs resemble “babies”, we tend to treat them that way,.
In human body language, this is a good thing.
In dog body language, very much *not*.
All the cuddling, cooing, carrying and so forth reinforces the dog’s notion that it, indeed, is the Alpha to which all other members of the pack owe deference.
My first suggestion would be, do not cuddle the dog at all until the aggression issue is resolved.
For the time being, do NOT allow the dog on the furniture, with or without you.
The dog sees its place on the sofa as being “equal to or greater” than *your* pack position and will definitely take advantage of that.
When it nips, do NOT punish it.
Simply pick it up and put it in its crate [or another closed off room, if you have no crate] and IGNORE it for a time.
When YOU feel like allowing it to be with you again, let it out.
If it snaps again, -immediately- reconfine and ignore it.
NO reaction is the “action” of an Alpha because the Alpha is “above” reacting to the lesser members of the pack.
Though it may be hard to do, since you do love the dog, do NOT offer affection unless the dog does something to -earn- it, whether it be simply getting off the sofa when told, sitting for a treat or pat...anything, really.
The dog must learn that “nothing in life is free”.
It will give your extremely insecure dog confidence in itself and your leadership.
[yes, it’s acting like a monster because it’s -afraid-...it knows the pack order is “wrong” and is not emotionally equipped to deal with the stress or responsibility of that]
You must never ever yell, scream or louldy chastise the dog.
The Alpha is always calm, confident and quietly self-assured.
So, either silently or with a firm, _low pitched_ voice let the dog know that the bad behvior will no longer be tolerated.
I have no idea how long the dog has been “alpha” so can’t give an time frame for how long it will take to reprogram its mind.
You will, however, wind up with a much happier, less stressed pet when it accepts that YOU are the pack leader and guardian.
Right now, the poor little thing feels responsible for guarding -its- human pack and it’s simply not mentally or physically equipped to do so.
If your dog ever reaches a stage where it comes to you and licks you *under* your jaw, you’ve got it made.
The rest of the pack always greets the leader with that same, subservient “kissing”.
If I can be of more specific help, feel free to write.