Does a wife touching her husband's penis, or greeting him and touching her, or kissing, invalidate their ablution, whether with or without an interposition, and with or without desire?

Touching the male organ does not invalidate ablution unless it is done with lust. So, if a woman touches her husband's male organ with lust, her ablution is invalidated. However, if it is without lust, it is not invalidated.

If the touch is made with a barrier, ablution is not invalidated, even if it is with lust. This is based on the hadith narrated by Abu Hurairah (may Allah be pleased with him) that the Prophet (peace be upon him) said: "If any of you touches his private parts with his hand without a barrier between them, he should perform ablution."

If a man shakes hands with his wife or kisses her, or she kisses him, the ablution of neither of them is invalidated, even if it is with lust, as long as nothing is discharged. This is based on what Aisha (may Allah be pleased with her) narrated: "The Prophet (peace be upon him) kissed one of his wives and then went out to prayer without performing ablution."