Can he marry the daughter of a woman who was breastfed by his mother?

If a woman breastfeeds a child, then this child becomes her child through radaa’ah (breastfeeding), and a brother through breastfeeding of all her children, whether those children were there before him or came later. 

Based on this, any woman who was breastfed by your mother is your sister through breastfeeding, and you are a maternal uncle to all her children. So it is haraam for you to marry her daughter, because you are her maternal uncle through breastfeeding. And the Prophet (peace and blessings of Allaah be upon him) said: “What becomes mahram (forbidden for marriage) through breastfeeding is that which become mahram through blood ties.” Narrated by al-Bukhaari, 2645; Muslim, 1447. 

It is haraam for a maternal uncle through blood ties to marry his sister’s daughter, and the same applies to the maternal uncle through breastfeeding. 

But it should be noted that becoming a mahram through breastfeeding can only be established through five well-known breastfeedings, because of the report narrated by Muslim (1452) from ‘Aa’ishah who said: ““When the Qur’aan was first revealed, the number of breast-feedings that would make a child a relative (mahram) was ten, then this was abrogated and replaced with the number of five which is well-known.” 

You state in your question that this woman breastfed from your mother twice, so we should note that the breastfeeding which makes the child a mahram is five feedings. 

Ibn al-Qayyim said in Zaad al-Ma’aad, 5/575: 

One breastfeeding (rad’ah) means when the child takes the beast and starts suckling, and then lets it go without being made to do so. That is one breastfeeding, because the Lawgiver referred to one breastfeeding in general terms, so it is to be interpreted according to custom, and this is the custom. If the child stops briefly in order to breathe or to rest or because of some distraction, then quickly goes back to the breast, this is regarded as one breastfeeding, just as when a person who is eating pauses briefly then quickly goes back to eating, this is not regarded as two meals, rather it is one. This is the view of al-Shaafa’i.  And if the infant moves from one breast to the other, this is one breastfeeding.  

See also question no. 2864  

Thus it becomes clear that the five breastfeedings could all take place in one sitting. 

If this woman was breastfed by your mother five times in this sense, then it is not permissible for you to marry her daughter, because you are her paternal uncle through breastfeeding. If she was breastfed less than five times, that does not mean that she is a mahram, so it is permissible for you to marry her daughter. 

If there is any doubt concerning the number of breastfeedings, whether it was five or not, there is no proof of the child being a mahram in the case of doubt. 

Ibn Qudaamah (may Allaah have mercy on him) said: 

If there is any doubt as to whether breastfeeding took place or not, or with regard to the number of breastfeedings, whether the number that makes the child a mahram was completed or not, this does not make the child a mahram, because the basic assumption is that he is not a mahram, and what is certain cannot be dispelled by what is uncertain. 

See also question no. 13357.

And Allaah knows best.