Is my wife's father, who is married to another woman, considered a mahram to me?

The Holy Quran stipulates the prohibition of four categories of women due to affinity (marriage relationship): the mothers of wives (prohibited upon the marriage contract), the daughters of wives with whom consummation has occurred, the wives of sons (whether biological or through suckling), and the wives of fathers. Consequently, the second wife of your wife's father is not prohibited for you unless there is another reason such as lineage or suckling. It is not permissible to shake hands with her or to be in seclusion with her.