Ive been in a physically abusive relationship and a narcissistic relationship, which both left me dealing with distress, severe anxiety, and trauma, to the point of a break down, and going for psychodynamic therapy.
No disrespect, but i think half the answers so far have been black & white thinking! Claiming she "assaulted" him with a slap after being shouted at is a bit over-dramatic and irrational. We don't really know the extent of the argument. We are just hearing one side of a story. A story lemonbabes has admitted to. But we still don't know if he was abusive or threatening. If she hits him again, then there's a problem, and he needs to leave. If he is continually shouting at her, then she needs to leave. All couples argue and fight, but that doesn't mean its an unhealthy relationship, its just their dynamic. I think its fair to give friends, partners, and family the benefit of the doubt, because you would want the same if you made a minor or detrimental mistake. Especially if it doesn't happen again.
Firstly, you have to define "violence", "assault" or "abuse", and there's a very fine line. To be classed as domestic violence, it has to be reoccurring physical abuse. Same with emotional abuse, it has to be reoccurring. And that includes gaslighting. You can't gaslight someone once. Its done repeatly over time.
Did you know that the "Child Law Advice" for the UK, America, and Canada states that it's not illegal to smack a child. Its legal discipline under certain circumstances, as long as it amounts to reasonable punishment. Babysitters aren't allowed to smack, unless given permission by parents. And that's not domestic violence. DV is something specific. Also, is it violence, assault, or abuse on your part if you attack an intruder who has broken into your house, use self-defence against a threatening situation in the street, or is it emotional abuse or emotional invalidation if you have an argument and say mean things to each other? None of that is violent, assault, or abuse. I got slapped as a teenager for back-chatting my mum. She's not a domestic violence abuser! Like i said, there's a very fine line under certain circumstances, otherwise half the mothers or fathers on here would be abusers!
Secondly, lemonbabe feels dreadful, and has took responsibility for her actions. Probably sees her slap as a mistake that won't happen again. That also shows some sort of empathy. And slapping cannot happen again, ok lemonbabes. But...
In response to lemonbabes original post: You have to realise that what you are doing is Triangulation. That's where you come onto this forum and involve other people in a two-person conflict, and you use indirect communication behind his back. Its passive aggressive. The goal of triangulation is deflecting tension, validation, and to divide & conquer. Most people are unaware that they do this behaviour. I think you have a slight superiority complex too, and are being too judgemental about the way he educates "his kids". Remember that he was a single dad, and has done a good enough job before he met you, and up until now with you. You's have been together 7 years, and you still see his kids as not yours, and you talk about you trying to instil some form of normality! Implying that his way isn't normal or not good enough. You're in it together, it isn't a competition. You're both step-parents, wither you're married or not. It should be equal and shared responsibility and parenting.
He turned mute (shut down) as a defence mechanism to avoid drama, stress or anxiety, and when you said "then he completely lost it", that's known as Reactive Abuse. And reactive abuse isn't "abuse", its him reacting to the stress of being ranted at or shouted at. It could also be reactive abuse in why you slapped him, as in you reacting to his verbal abuse (shouting). In other cases, an example of reactive abuse is if a toxic person bully's someone physically or emotionally, and the victim reacts with anger, verbal abuse or an attack (usually in public), then the bully plays the victim. Its complex and complicated.
If he's now refusing to talk about it, then you need to figure out wither he just needs time to himself to de-stress, is giving you the silent treatment, or wither he is stonewalling you. Sometimes the silent treatment is a way to avoid conflict, but it never solves anything, it just builds up resentment. If he's stonewalling you, that usually means its his way of punishing you, but that usually lasts for days, and is a refusal to ever talk about it, so its good to know the difference between those three.
You talk about the red flags in his behaviour, but you have to remember that a red flag actually means danger. If there's danger, you need to leave, not just for your sake, but the kids safety. Since the rise of social media, red flags are exaggerated online, and everything seems to be a red flag these days, when its not. Relationships are also portrayed on social media as perfect, when that's not reality. All relationships have conflicts, and without conflict, nothing is being decided. And that's where you set boundaries. So, you's should do that as soon as possible. Sit down and talk about everything.
I think you need to self-reflect too. Look at your part in all this instead of just blaming him for lack of normality. You need to communicate better with him too, especially if you want more support. Apologise to each other, and try not to let arguments ruin your relationship, and never raise your hands. Consider couple councilling. If he doesn't consider that option or isn't supportive in general, then why are you together!