He is not sure about the meat that his mother buys

Firstly: 

If the meat has been slaughtered by one of the People of the
Book (a Jew or a Christian) and we do not know the method of slaughter, but
most people in the country kill meat by means of electric shock or by
slaughtering it for someone or something other than Allah, it is not
permissible to eat that meat, on the basis of what is usually the case. The
same applies if one is not sure whether the meat was slaughtered properly or
killed by means of electric shock. That is because of the report narrated by
al-Bukhaari (5485) and Muslim (1929) from ‘Adiyy ibn Haatim (may Allah be
pleased with him) from the Prophet (blessings and peace of Allah be upon
him) who said: “If you release your (hunting) dog and say the name of Allah,
and (the dog) catches (the game) and kills it, then eat, but if (the dog)
ate (some of it), then do not eat, because he only caught it for himself. If
another dog joins him over whom the name of Allah was not mentioned, and
they caught it and ate from it, do not eat, for you do not know which of
them killed it. If you shoot an arrow and you find (the game) after one or
two days with nothing but the mark of your arrow on it, then eat, but if it
fell into water, do not eat it.” 

According to a report narrated by Muslim: “When you shoot
your arrow, mention the name of Allah. Then if you find it (the game) dead
then eat, unless you find that it has fallen into water, in which case you
cannot know whether it was the water that killed it, or your arrow.” 

The Prophet (blessings and peace of Allah be upon him)
forbade eating if there is any uncertainty as to whether the meat was
slaughtered properly in accordance with sharee‘ah because of the hunting dog
being joined by another dog, or because of the target animal falling into
water and the possibility that it died by drowning. 

Al-Nawawi (may Allah have mercy on him) said in Sharh
Muslim: The words of the Prophet (blessings and peace of Allah be upon
him): “If you find with your dog another dog and it joined in killing (the
game), Do not eat because you do not know which of them killed it.” This
states an important principle, which is that if there is any doubt as to
whether the animal was slaughtered in the permissible manner, it is not
halaal, because the basic principle is that it is haraam. This is a point on
which there is no difference of scholarly opinion. End quote. 

Al-Haafiz Ibn Hajar said in Fath al-Baari: The words
“if it fell into the water, do not eat it” – the reason for the prohibition
on eating it is to be taken from the phrase above, because in that case
there is doubt as to whether it was killed by the arrow or by drowning in
water. If it is established that the arrow struck it and it died, and it did
not fall into the water until after it was killed by the arrow, then it is
permissible to eat it. al-Nawawi said in Sharh Muslim: If the game is
found in the water, drowned, it is haraam according to consensus. End quote.
al-Raafi‘i said that if he reaches it in time (before it dies) and cuts its
throat for example, then he has slaughtered it in the proper manner. His
opinion is supported by the report narrated by Muslim, “you cannot know
whether it was the water that killed it, or your arrow.” This indicates that
if he knows that his arrow is what killed it, then it is permissible. End
quote. 

For more information please see the answer to question no.
10339. 

Secondly: 

If your mother or someone else brings haraam meat, it is not
permissible to eat it, because Allah, may He be exalted says (interpretation
of the meaning):

“Forbidden to you (for food) are: Al-Maitah (the dead
animals – cattle – beast not slaughtered), blood, the flesh of swine, and
that on which Allâh’s Name has not been mentioned while slaughtering, (that
which has been slaughtered as a sacrifice for others than Allâh, or has been
slaughtered for idols) and that which has been killed by strangling, or by a
violent blow, or by a headlong fall, or by the goring of horns – and that
which has been (partly) eaten by a wild animal – unless you are able to
slaughter it (before its death) – and that which is sacrificed (slaughtered)
on An-Nusub (stone altars). (Forbidden) also is to use arrows seeking luck
or decision; (all) that is Fisqun (disobedience of Allâh and sin).”

[al-Maa’idah 5:3]. 

You have to be gentle and polite when explaining why you do
not want to eat this meat, and try to make your mother happy by eating other
food that she offers; bring her some halaal meat to cook when you are there
and try to convince her of the importance and benefits of eating halaal meat
and the harmful effects of eating meat that was not slaughtered in the
proper shar‘i manner. This is due to the rights that she has of respect and
kind treatment. 

See also the answer to question no.
172

And Allah knows best.