Despite our nursing, my daughter isn't getting any better.

Literal

Daughter [topic-は] our [possessive-の] nursing [despite-にもかかわらず] slightly not-good [explanatory-のです].

~にもかかわらず ('despite') + 少しも ('not even a little') + negative creates a strong 'not at all.' 少しも is always paired with a negative predicate for 'not even slightly.' A worried family statement.