This isn't him having a temper. It's manufactured rage to scare and intimidate you into doing what he wants. It's coercive control and he is in complete control of himself. This is how he wants things to be.
Freedom Programme can help you make sense of it all, including the impact it's had on you and the children, how they and you will heal after leaving (when you're ready) and what a healthy relationship would have looked like.
They won't judge you, won't tell you to leave, and won't even ask you to share anything about yourself. It's an information course, not therapy, but they're supportive and it's all confidential. The group course is free to attend or there is an online version for a small charge (£10), but I would recommend the group if you can.
Www.freedomprogramme.co.uk
This isn't about any of the things you supposedly do wrong, it's about his desire to feel powerful by controlling you and making you walk on eggshells. You could spend the rest of your life trying to be perfect according to what he kicked off about today, but he will keep changing the goalposts so that you've always done something wrong.
That feeling you have of walking on eggshells will be shared by your children. As children, they don't have the perspective you have and their only way to make sense of what's happening is that it's their fault and because they did something wrong. That's just how children understand the world and is most likely driving their worries about him not wanting to be a family - they're scared it's something they've done.
Protecting them from growing up in an abusive, volatile home where they can never relax or feel safe because they never know what will make dad explode at someone is the most important thing here.
Be clear with them that it wasn't their fault and how he behaved was wrong. They won't benefit if you try to cover up for him. It will just confuse them.
Allow yourself to grieve for the life you dreamed you were going to have with him. I'm really sorry, because he won't get better and you can't change him.
Life does get better once you're not living like this anymore, but you need to be ready to make the change first. Consider starting with the Freedom Programme - doesn't mean you have to leave, it's just information gathering and then you decide what you want to do with what you learn.