If the mother inherits from her deceased daughter, then the mother dies, does what she inherited from her daughter go back to the children of that daughter?

Praise be to Allah.

If the mother inherited from her deceased daughter, then the mother dies, her share of her daughter’s estate does not go back to the children of this daughter and they do not inherit from her; rather it is inherited by her (the mother’s) legitimate heirs who inherit from her by means of their allocated share (fard) or by being residuary heirs (‘asaabah). As for her daughter’s children, they do not inherit from her because they are dhawu’l-arhaam (distant relatives through the female), and dhawu’l-arhaam do not inherit except in the case when there are no heirs with allocated shares or residuary heirs.  

Ibn Qudaamah (may Allah have mercy on him) said: If the deceased leaves behind residuary heirs or heirs who are entitled to an allocated share, they take all the wealth and there is nothing for dhawu’l-arhaam. This is the view of most of those who say that dhawu’l-arhaam may inherit. End quote. al-Mughni, 6/209 

The questioner says “they are the most entitled of people to their mother’s wealth.” But it should be noted that the wealth is not regarded as belonging to their mother any more, because when a person dies his wealth or property is transferred to his heirs and Allah, may He be exalted, has given each person his right. 

He also says “because they are orphans from their mother's side”. This is also subject to further discussion, because the yateem or orphan (in shar‘i terminology) is the one whose father has died and is below the age of puberty. Ibn al-Sikkeet said: The orphan is the one whose father has died; the one who has lost his mother is not called an orphan. End quote. 

See: al-Mawsoo‘ah al-Fiqhiyyah, 45/254 

And Allah knows best.