Is what the questioner did—refusing to lend her sister-in-law her shoes to go to a mixed-gender wedding, on the grounds that it would be aiding in sin—correct?

It is not permissible for a girl to attend mixed wedding parties due to the possibility of falling into forbidden acts or sitting with transgressors. You were right not to help her go, and you should strive to guide her and urge her towards righteousness and staying away from places of disobedience. Be sure to remove any misunderstanding regarding accusations of stinginess by offering some food items or things that are not used in forbidden ways. Increase your prayers for them, and seek help from your husband and some righteous female callers to Islam.