There is a good chance neutering would be a waste of money. Even if you do it early, it really plays only a small part in shaping a dog's temperament. It is a commonly suggested quick fix that people throw out there when they see behavioral problems, because it is better to lay your hopes on something like that than on changing the way you live with your dog.
I would say there is a direct correlation between the way people live with these smaller, cuddlier toy-type breeds and the dog's behavioral problems. Unfortunately alot of them develop serious behavioral problems because the owners feel like any sense of firm, strict discipline will break the dog in half. Factors that worsen the issues include the dog spending too much time in the owners' arms or lap, and attempts to calm them and take them out of attack mode using soft speach and physical affection. In other words, many of these dogs spend much of their lives at or near eye level with other humans, while their owners unknowingly nurture a dominant state of mind by giving them positive physical touch while they are in the middle of misbehaving. It increases the chances that they will become dominant, obnoxious, and in some cases aggressive. I would wager good money that at some point this dog has done something obnoxious and inappropriate, and the first thing you did in response was grab him in your arms and pick him up off the floor.
If this were a Pittbull or Rottweiler, I would, in a way that does not cause permanent injury, make the little bugger feel like its life was about to end every time it exhibited this type of behavior. It would be no different with this being a 'Pekepoo.' He would loose all of his un-supervised freedom in my home, spending most of his time in a crate or else by my side on a leash with a corrective collar. I would rattle his brain with a high level leash correction every time he gowled, bit me or anyone else, or even looked at one of the children wrong. While doing it I would tell him NO in a calm, but assertive tone of voice. Often times a dog with a dominant mindset won't respond well to positive reinforcement. Before you can use that concept, the dog first has to learn that the bad behavior it exhibits won't be tolerated for one more second, and will always bring swift, powerful, memorable corrections. Before you can even start to work with a dog like this, you first have to lay a basic groundwork where it's first desire in life is to please you, and its number one priority in life is to avoid pissing you off.
He would never get a single treat again without sitting calmly to wait for it. He would get enough exercise on a daily basis to make him want to sleep for a long time afterward. It shouldn't be wild romp time in the yard, it should be calm, steady, continuous exercise under your supervision. If you aren't physically capable of doing this anymore, you need to put the dog on a treadmill and train him to use it.
Obedience training would begin again from the ground-up, as this will help remind the dog of its place in the home. And I would start reinforcing some basic pack structure rules. The dog would no longer get to enjoy any prime resting spots that are normally reserved for humans. He wouldn't get any couch time or bed time. He would probably be in a crate while I ate dinner, and be fed after me.