Praise be to Allah.
It is haraam for you to sit with your wife’s sister or any other non-mahram woman on her own. The Messenger of Allaah (peace and blessings of Allaah be upon him) said: “No man is alone with a woman but the Shaytaan is the third one present with them.” (Narrated by al-Bukhaari, 9/290; Muslim, no. 1341; Ahmad, al-Musnad, 1/222 and 346).
It is haraam for a man to be alone with a woman who is not his mahram. Your wife’s sister is a stranger (i.e. non-mahram) to you, because if you were to divorce your wife, it would be permissible for you to marry her (her sister). So she is not one of your mahrams. With regard to breaking wudoo’, it is only broken by touching a woman with desire. If a man touches a woman with desire, this breaks his wudoo’, whether the woman is a non-mahram or otherwise. The kind of touching which breaks wudoo’ is physical touching with no barrier in between. This is what has been stated by the scholars. And Allaah knows best.
Fataawa Shaykh ‘Abd-Allaah ibn Humayd, p. 48
The verdict on shaking hands and touching a non-mahram woman (a woman who one can marry) has been stated earlier under Q# 2459.