Acceptance is not a requirement or condition for getting a divorce in places with no fault divorce laws. Just as the justice system does not force or require you to marry. It will not force you to remain married when you no longer desire to do so.
However, you cannot force him out of home in which he has joint legal ownership. You can force a sale , but you cannot force him to leave, and if he is not overly concerned about damage to his credit rating, you cannot force him to continue making mortgage payments.
You are correct in saying that your living arrangement was not uncommon, but sadly the outcome for many many women who enter into such arrangements, the outcome is all too common.
You need 2 things immediately. You need legal representation and you need a job. He will have to provide some amount of support for his children; but you too will be expected to contribute to their support. Your support contribution will now need to be in actual currency rather than in services alone.
You children are so young that being moved to another home won't be nearly as unsettling as you might think. Keep in mind that old promises and decisions are not likely to carry any weight in a Court that will be looking to split your assets equally and absent some demonstrably negative information will give each of you 50/50 custody.
In essence, start planning for your new life with the awareness that you will no longer have a partner who pays while you manage and serve. You will now have to manage serve , and work as well, but the upside is that you will no longer have to live in a situation that you found to be unbearable.
He was only contributing money in your life, and now he will be contributing even less of that.
You can and will get your bearings and get it all sorted. It will just take some time to get to that place.