OP
How can you be helped into leaving your abuser?. He does not deserve any more chances from you. This is who he really is and he is not going to change.
Abuse is indeed not a relationship issue nor is it about communication or a perceived lack of. It's about power and control.
He can and does control himself around other people in the outside world.
He has a problem with anger, YOUR anger, when you call him out on his behaviour. And AM classes are NO answer to domestic violence which is what is being described here.
He is indeed a textbook abuser right down to even how others think of him. To those in the outside world he is Mr Nice Guy but your kids see him as grumpy and snappy. Closer friends see him as being sometimes moody. You do know that moodiness is an example of emotional abuse. You are his emotional punch bag. He does not have to be violent physically to hurt you; words are doing that and he has you cowed. Am certain too your kids hear all that from him towards you in the home so they are being subjected to this as well. They are indeed telling you that their dad is grumpy and moody. His apologies are meaningless and he is really showing you the nice/nasty cycle of abuse which is a continuous one.
And of course his parents are not great either; no surprise there because the rotten apple did not fall far from the rotten tree.
Do you really think that such a man would be open to be counselled?. No not a bit of it. He likely thinks there is nothing wrong in how he treats you and in turn his children. This is also deeply ingrained within his psyche and he would need years of therapy, not mere months. And he is most unlikely to stick at it again because he thinks there is nothing wrong with him. Its everyone else's fault expect his own.
Such men hate women too. All of them.
There is never any one good time to leave but I would be very brave here and start seeking legal advice on the quiet. You are married to this man and thus have rights in law. Do this before January if at all possible as that is the Solicitors busiest month. Also knowledge here is power for you.
I doubt very much the atmosphere at home is at all condusive to studying for exams and besides which these can be retaken if needed. They are absolutely not the be all and end all. Saving money also takes time and the longer you remain with him the worst potentially it will become for you and your kids. This is NOT the relationship model to leave them because they could well copy this same model as adults. Teach them properly that the only acceptable level of abuse in a relationship is none.
I would also suggest you reach out to Womens Aid, they have an online chat facility too. At the very least I would urge you to visit Boots and ask for ANI, the staff will direct you to domestic violence support services that they have in their branches.