The author of the dog article recommended an approach by Becky A Bailey which is called Conscious Discipline and outlined in the book "Easy to Love, Difficult to Discipline". The title is a bit yuck IMO but I looked into the theory and it is really very good.
The idea behind the name conscious discipline is wrapped up in several concepts.
First of all we tend to automatically parent in sort of an unconscious way. We naturally react the way that our parents did to us, we generally don't know how to put conscious thought and proactive measures in place. So the idea of "conscious" discipline is both about changing that old learned automatic response to something that is more logical and thought out and effective.
Second, much parenting advice is very one-size-fits-all almost like it could be applied automatically by a robot. "Oh just tell him no" "Take away his TV time" "Make sure he knows who is boss" "Count to 3 and then give a consequence" etc. But for effective communication you need to be very present and cognizant of what is actually going on with your child. So, paying conscious attention. Being curious. Looking at what they are actually doing and why.
Third the idea of discipline - we often shy away from this thinking it means something harsh, punishment. But think about the discipline of martial arts or meditation. Think about the discipline of a swimmer or a gymnast committing to practice every day. In this way it's about repeated practice and consistency and building good strong habits and norms. So you have the discipline of yourself as a parent committing to being conscious and proactive, and that leads to the discipline of the child who is learning self restraint and learning what is acceptable behaviour.
In this situation particularly it would probably be counterproductive to be very harsh and intense and loud with your son because this is just going to upset the dog as well. You don't want to create a situation where the dog comes to see any interaction with your son as even more stressful because he is expecting it to result in shouty scary mummy. Your aim is to reduce stress for the dog!
MN has a lot of parents with differing parenting approaches and the idea that children are little hellions and you have to stamp out perfectly ordinary toddler behaviour lest it grows like an angry monster is popular, but it's not something that I would subscribe to. Which does not mean that you have no boundaries at all, it just looks a bit different how you would want to approach things. Setting up for success is hugely effective IME and if the dog issue is the number one issue of the moment, then it makes sense to really focus on this one issue by doing all of the things that help set that up for success.