She died and did not leave behind anyone but the daughter of a brother of hers; does (that niece) inherit from her?

The brother’s daughter comes under the heading of dhuwil
arhaam (relatives), and the scholars differed as to whether they may
inherit. 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: 

The phrase dhuwil arhaam refers to any relative who is
not allocated a share of inheritance and does not inherit by virtue ta‘seeb
(being a close male relative on the father’s side). 

All females apart from sisters – such as paternal aunts,
maternal aunts, daughters of brothers, daughters of sisters, and daughters
of paternal uncles – come under the heading of dhuwil arhaam. 

The scholars differed as to whether dhuwil arhaam may
inherit. Maalik and ash-Shaafa‘i said: They do not inherit. Abu Haneefah and
Ahmad said: They do inherit, on condition that there is no ‘aasib (male
relative on the father’s side) or heir who is allocated a share of
inheritance to whom the remainder of the estate may be given. This was
narrated from ‘Umar, ‘Ali, Abu ‘Ubaydah, ‘Umar ibn ‘Abd al-‘Azeez, ‘Ata’ and
others, and is the correct view, because Allah, may He be exalted, says
(interpretation of the meaning):

“But kindred
by blood are nearer to one another regarding inheritance in the decree
ordained by Allah. Verily, Allah is the All-Knower of everything”

[al-Anfaal 8:75].

And the Prophet (blessings and peace of Allah be upon him)
said: “The son of a people’s sister is one of them.” Narrated by al-Bukhaari
(3528) and Muslim (1053). And he (blessings and peace of Allah be upon him)
said: “The maternal uncle is the heir of one who has no heir, paying blood
money for him and inheriting from him.” Narrated by Abu Dawood (2899);
classed as hasan by al-Albaani in Saheeh al-Jaami‘ (6147) 

The possible scenarios regarding dhuwil arhaam are as
follows: 

There is only one such relative who may inherit. He (or she)
inherits all of the wealth by virtue of being a relative on the father’s
side, or by means of being entitled to inherit and by taking what is left
after taking his (or her) allocated share. 

If someone dies and leaves behind the daughter of a full
brother, then she inherits all of the wealth by virtue of virtue of being a
relative on the father’s side. 

If he dies and leaves behind the daughter of a brother
through his mother, then she inherits one sixth as her allocated share of
inheritance and she inherits the rest because there are no other heirs. End
quote. 

Based on that, your mother inherits all the wealth of her
paternal aunt. 

And Allah knows best.