Thank you for writing. You asked for my advice. — In my opinion you and your kids should not have to put up with this behavior. What you are describing in verbal and emotional abuse. No one should have to live with such unpredictable and unreasonable anger. You and your kids should not have to walk on eggshells all the time in your own home out of fear that you will set him off.
There is no instruction manual for learning how to tolerate intolerable behavior. Your job isn’t to “appease” him. Ideally, he would join with you in making a loving and safe home for your whole family.
I don’t have enough information to comment on whether he is mentally ill. Regardless, illness is never an excuse for hurting one’s family. A diagnosis is only a descriptor for what seems to be wrong. It is up to the patient to then go forward with treatment to be successful in family life, at work, and in friendships.
Those who work hard at getting well earn the respect and support of those around them. Family and friends and even work places do make allowances for someone who is trying hard to change. Those who expect to be tolerated and loved no matter how badly they behave end up isolated and lonely, having damaged relationships beyond repair.
Since your husband doesn’t take therapy seriously, there is no point it trying it with him again. But there is definitely a point to you going for therapy on your own — and for possibly involving your kids. You need and deserve to have a supportive professional in your life who can help you decide how best to take care of yourself and your children.
I also suggest that you see if there is a chapter of NAMI (National Alliance on Mental Illness) in your area. NAMI is a grassroots organization where people who are living with mental illness and their families can get information and support. They also have a helpline. If you haven’t already, do check their website for information about the services they offer.
I wish you all well,