Is what the wife's sister does, in not reciprocating kindness with kindness, correct? And should the wife continue to maintain ties with her despite her lack of reciprocation?

The wife's sister is not among the kin whose ties you are obliged to maintain, rather, it is your husband's duty to maintain ties with her. Your assistance to your husband in maintaining ties with his kin is a righteous deed. Your maintaining ties with her is a good act for which you will be rewarded, and you should continue to maintain ties with her and honor her seeking the pleasure of Allah, even if she falls short in her duty towards you, in accordance with the Prophet's (peace be upon him) saying: "Shall I not tell you about the noblest morals of this world and the Hereafter? To forgive him who wronged you, to give to him who deprived you, and to maintain ties with him who severed them from you."