Adjectives only inflect strongly if they come without an article (but they may follow a numeral). When the attributes qualify a feminine or plural noun, it also doesn’t matter whether the article is definite (die) or indefinite (eine), because weak and mixed inflection are the same for these two genders/numbers.
mit requires dative case, but you got that correct anyway. Therefore it is mit einer kräftigen Hand and alternatively mit der kräftigen Hand or more abstract mit kräftiger Hand. For female or plural, strong inflection is the same as article and pronominal inflection, when you accept that d+ root and +e suffix result in die.