The wife of your wife’s father is not a mahram for you

The wife of your wife’s father is not
considered to be a mahram for you, so it would be permissible for you to marry her, because whether or not a person is a mahram can only be proven
by a text of sharee’ah, and there is no text to state that this person is a mahram. Rather, when Allaah listed the women who are mahrams, He
stated that all others are permissible for marriage. Allaah says (interpretation of the meaning): 

“All others are lawful”

[al-Nisa’ 4:24]

Not only that, it is also permissible to be
married to a woman and her father’s ex-wife at the same time, according to the majority of scholars. 

Ibn Rajab al-Hanbali said: 

Being married to a man’s ex-wife and his
daughter from another wife at the same time is permissible according to the majority but is makrooh according to some of the salaf. 

Jaami’ al-‘Uloom wa’l-Hukam,
p. 411 

Imam al-Shaafa’i said: 

If a man is married to the daughter of a man
and the ex-wife of her father (at the same time), Abu Haneefah (may Allaah have mercy on him) said that this is permissible, and we heard that
‘Abd-Allaah ibn Ja’far did that. 

Al-Shaafa’i (may Allaah have mercy on him)
said: There is nothing wrong with being married to a man’s ex-wife and his daughter from another wife. 

Al-Umm, 7/155 

Imam Ibn Hazm said: 

It is permissible for a man to be married to a woman and to the ex-wife of her father and the
ex-wife of her son and the daughter of her paternal uncle at the same time, because there is no text which states that this is haraam. This is the
view of Abu Haneefah, Maalik, al-Shaafa’i and Abu Sulaymaan. 

Al-Muhalla,
9/532. 

Ibn Qudaamah said: 

There is nothing wrong with being married to
a woman who was the wife of a man and his daughter from another wife. 

Most of the scholars say that it is
permissible to be married to a woman and her stepdaughter at the same time. ‘Abd-Allaah ibn Ja’far and Safwaan ibn Umayyah did that. This is the
view of all the fuqaha’ apart from al-Hasan, ‘Ikrimah and Ibn Abi Layla; it was narrated that they regarded it as makrooh. 

Allaah says (interpretation of the meaning): 

“All others are lawful”

[al-Nisa’ 4:24]

And because they are not related, they are like two strangers. And because marrying two
closely-related women at the same time is forbidden lest there be a severing of family ties between those who are closely related. There is no
such relationship between these two, so their case is different from what has been mentioned.

Al-Mughni, 7/98 

Based on this, then the wife of your wife’s
father is not counted as one of your mahrams, rather she is a “stranger” to you, so you may not shake hands with her or be alone with her or
travel with her. 

And Allaah knows best.