Your boss is not going to change his mind.

His opinion of you may have little to do with you, and he is going to prove to himself that he was right for the rest of days.

What you need at this moment is to take responsibility for yourself, not to off-load that onto the "children's welfare." When you make yourself more "valuable", your children will benefit.

When having a choice, take the path where you can more be in charge.

Everything comes with a price. Which one to take depends on what you value.  Others, who value different things, cannot help much in your decision-making.