If the husband is in financial hardship and the wife is the primary provider for the family, and the husband's mother is financially well-off, is the husband obligated to give his intermittent income to his mother, or to his wife, or should he divide it between them?

The husband is not obligated to spend on his mother if she is self-sufficient. Rather, he is obligated to spend on his wife in a reasonable manner. He must pay his wife the maintenance for the period during which he did not spend on her, and this maintenance becomes a debt upon him.