He sounds abusive and like a horrible father.
My dad was abusive, mainly emotionally. I ended up having to get a non-molestation order against him (like a restraining order). Even he managed to teach me to ride a bike without getting frustrated and throwing it.
He'd get angry over stupid things and have tantrums. It was so absurd some of the things that set him off we used to laugh about it (my mum, brother and me). But it wasn't really funny. It was a defence mechanism we used to cope with how unpredictable and unreasonable he was. You never knew what might set him off.
It was childish and silly, but he was also an adult man, much bigger than us and he could be frightening. We laughed to try to deal with the fear and reassure ourselves, and try to convince ourselves we were okay. Otherwise we'd be consumed by it.
Also... children will naturally love their parents and look for affection and attention. That doesn't mean I adored him (while I loved him I also disliked him and viewed him with contempt as he was more emotionally immature than his own children and was cruel to my mum), I just didn't know any different to an abusive father and was trying to protect myself and get him to be more caring towards me.
He could also buy me nice presents and was very funny. When I was very young he used to play with me a lot. My mum insisted he was a good dad due to things like this and him not being abusive ALL the time, and aiming the bulk of abuse at her...of course I'd be listening and watching, taking in that a relationship involved being talked to like dirt by men. That this was normal, as was having to accept being shouted at disrespected myself when he got in a mood.
I learned to change my behaviour to be more accommodating of him and to avoid worse abuse being targeted at me. I have an incredible tolerance now for mistreatment. I will seem calm though the most terrible things. I have been conditioned for this. -- It's horribly unfair.
It's abusive to abuse someone in front of a child, especially a child's mother. It is damaging. It must have been very confusing for your children to be left with you in Burger King (I assume with no other means of transport) because daddy had an inexplicable temper tantrum, and then mummy lied about it. -- This sort of thing I used think felt wrong, but then mum acted like it was actually normal and okay, and it really troubled me. I wanted her to confront the actual problem and protect us.
My dad was disrespectful to my mum but wasn't totally horrible to her in front of others usually, unless he was drunk. He was smart enough to know that would make him seem like an abusive man and it might raise concerns. He mostly tried to do it in a way where it seemed like a joke, so it troubles me your husband is so open with his mistreatment.
Not talking to children in a caring and developmentally appropriate way can be a sign of an abuser, too. I used to be spoken to like a little adult. It shows a lack of empathy and affection.
I really think you are minimising how bad this actually is for you and the children. You are being abused, as are they.
We thought my dad might have a mental health problem (he was sectioned and even in a mental health hospital for a while) but he saw mental health professionals and they basically decided he was honestly just a horrible person. -- I know, it's just so difficult to understand someone like this it seems it must be something like that, but abusers are just horrible for the control and power. In my dad's case he clearly had low self esteem and my mum tried to rescue him. He only had mental space for himself though, due to his issues. He doesn't have properly developed empathy. That's what allows him to be cruel. He doesn't care enough for you all not to be and only about himself and his emotional reality.
Women's Aid were amazing and helped my family so much. I'd highly recommend contacting them. Do be careful how you leave if you chose to. It's often better to do it secretly and then handle the abuser through a solicitor. Abusive men who have not yet been violent can escalate and react in ways they never have before when you try to leave.
I get the A word is hard to face up to, it's a big thing to accept you are or have been abused. It's more comforting to down play it and easier to keep your old sense of yourself and your reality, but you deserve to be happy and safe. So do your children.