Financial Responsibility in Marriage

I am a housewife, mostly because my husband prefers it that way. I have a very small income of my own, but in general, my husband pays for everything.
Recently we have been having frequent disagreements about money that almost always relate to my children from a previous marriage.
He doesn’t really mind spending money on my 4 year old daughter who lives with us full time, but he is strongly opposed to spending any money on my 17 year old and 21 year old children.
His solution was that I should never spend any money on them.
I understand his reasoning, but I don’t feel like that’s realistic (he genuinely means no money, ever, not even birthday gifts).
My solution was that I will only spend money on my adult children from my income.

What is the correct solution?