His wife is accusing him of harassing her sister and he said to her: If I touch your sister then our marriage is invalid. Then he touched her again with desire
You should realise that what has happened of you touching your wife’s sister with desire is something that is undoubtedly haraam. It comes under the heading of zina (adultery) of the hand, of which the Messenger of Allah (blessings and peace of Allah be upon him) spoke. Zina is not only zina of the private part; rather there is also zina of the hand, which is haraam touching, and zina of the eye, which is haraam looking, even though it is zina of the private part that incurs the hadd punishment. After this, how can you claim that there is no reason for suspicion and that your wife has no right to be suspicious about you. What you are doing is very suspicious and is indicative of bad intentions and a bad attitude.
It says in the hadeeth narrated by Abu Hurayrah from the Prophet (blessings and peace of Allah be upon him) that he said: “Allah has decreed for the son of Adam his share of zina, which he will inevitably get. The zina of the eyes is looking and the zina of the tongue is speaking. The heart wishes and hopes, and the private part confirms that or denies it.”
Narrated by al-Bukhaari, 5889; Muslim, 2657.
According to a version narrated by Muslim: “The zina of the eyes is looking, the zina of the ears is listening, the zina of the tongue is speaking, the zina of the hands is touching, and the zina of the foot is walking. The heart longs and wishes, and the private part confirms that or denies it.”
The Messenger of Allah (blessings and peace of Allah be upon him) warned against touching a non-mahram woman and said: “If one of you were to be stabbed in the head with an iron needle, that would be better for him than touching a woman who is not permissible for him.” Narrated by at-Tabaraani from the hadeeth of Ma‘qil ibn Yasaar; classed as saheeh by al-Albaani in Saheeh al-Jaami‘, no. 5045.
If this is a sin and crime in the case of any woman, and means that you cannot be trusted, then how about if it involves your wife’s sister, who is haraam to you so long as her sister is your wife?
What you must do is ask Allah, may He be exalted, to forgive you for this sin and repent to Him; you must also resolve not to do that again and to block all ways that may lead to fitnah or temptation with this woman. So do not be alone with her, and do not be with her in any place or in any situation that could lead you to go back to what you had been doing.
Moreover, there is no need for you to speak to her, with or without desire; if there is any reason for you to speak, her sister – namely your wife – can take care of it.
With regard to your saying to your wife, “If I touch your sister then our marriage is invalid (‘nikah breaks’),” this is a metaphor for divorce. In the case of metaphors, divorce does not take place unless there was the intention of divorce, as we have explained in fatwa no. 120947
So long as you did not intend divorce thereby – as you say in your question, trusting what you said – then divorce has not taken place.
And Allah knows best.