She is very anxious because the second wife may inherit the same as her
Question

                My father took a second wife a while ago, after being married to my mother for twenty-five years. Since that time my mother has been depressed because this woman may inherit the same as her, and she says: I have been suffering all these years, then this woman comes and gets the same inheritance as I will get; I will never accept that. When I asked a Shaykh about this matter, he said that in his country there is a custom in inheritance whereby the second wife does not inherit from the property that was present during the man’s first marriage and during the second marriage, both wives inherit from whatever extra property there is. Is this correct? Is there any other solution?.
Praise be to Allah.
    Firstly: 

    Allaah has permitted a man to be married to one or two, up to 
    four, at any one time, as He says (interpretation of the meaning): 

    “And if you fear that you shall not be able to deal justly 
    with the orphan girls then marry (other) women of your choice, two or three, 
    or four; but if you fear that you shall not be able to deal justly (with 
    them), then only one or (slaves) that your right hands possess. That is 
    nearer to prevent you from doing injustice”

    [al-Nisa’ 4:3]

    If a man takes a second wife then he dies, both wives share 
    the inheritance, and one does not get more than the other. They are both 
    included in the verse in which Allaah says (interpretation of the meaning): 

    “their (your wives) share is a fourth if you leave no 
    child; but if you leave a child, they get an eighth of that which you leave 
    after payment of legacies that you may have bequeathed or debts”

    [al-Nisa’ 4:12]

    This is the ruling of Allaah, Who is the wisest of Judges and 
    the most Merciful of those who show mercy. Every believing man and woman 
    must submit to this and humble themselves, and not feel resentment towards 
    the ruling of Allaah and what He has prescribed in sharee’ah, as Allaah says 
    (interpretation of the meaning): 

    “It is not for a believer, man or woman, when Allaah and 
    His Messenger have decreed a matter that they should have any option in 
    their decision. And whoever disobeys Allaah and His Messenger, he has indeed 
    strayed into a plain error”

    [al-Ahzaab 33:36] 

    “But no, by your Lord, they can have no Faith, until they 
    make you (O Muhammad ) judge in all disputes between them, and find in 
    themselves no resistance against your decisions, and accept (them) with full 
    submission”

    [al-Nisa’ 4:36]

    Our advice to your respected mother is to fear Allaah and to 
    accept what He has decreed, and to have certain faith that the ruling of 
    Allaah is just, merciful, good and right. “And who 
    is better in judgement than Allaah for a people who have firm Faith?” 
    [al-Maa'idah 5:50]. 

    She should be very wary of turning away from the ruling of 
    Allaah or rejecting it, or feeling anxious because of it, because that is a 
    serious matter. 

    No one knows whether he will be an heir or the one from whom 
    others inherit, so why should he become so attached to worldly things and 
    feel content with them whilst losing his religious commitment by turning 
    away and not accepting what Allaah has decreed? 

    Secondly: 

    The property that was present during the first marriage falls 
    into two categories: 

    1 – That which has passed from the husband’s possession to 
    the wife’s by being given as a gift or because it is part of her dowry etc. 
    This is the property of the wife and does not form part of the husband’s 
    estate if he dies. For example, if the husband gives his wife a house, gold 
    or furniture, or if the gold or furniture was part of the dowry, as is the 
    custom in some countries. 

    2 – That which belonged to the husband and still belonged to 
    him until he died. This is included in his estate and it should be divided 
    among all his heirs according to their shares. For example, if the husband 
    had real estate or money, which he took possession of before his first 
    marriage, or after that, or after his second marriage, and it did not cease 
    to be his property by being given as a gift, etc. This is included in his 
    estate after he dies. 

    Perhaps what the Shaykh you refer to said applied to the 
    furnishings of the house etc, which in some countries people regard as being 
    part of the wife’s dowry, so it belongs to her and is not included in the 
    husband’s estate. 

    Similarly, the delayed portion of the dowry belongs to the 
    wife and she may take it from the estate before it is divided, because it 
    comes under the same ruling as a debt. 

    Some husbands give the first wife some money or property that 
    is to belong to her. If this is done before the second marriage takes place, 
    there is nothing wrong with it, but if it is done after that it is not 
    permissible unless he gives the second wife something similar. The Standing 
    Committee for Research and Issuing Fatwas was asked: I have two wives and I 
    want to buy gold for one of them as a gift. Is it permissible for me to do 
    that? Or is this regarded as not treating co-wives fairly? Please note that 
    I am not falling short with regard to the rights of the other wife. 

    They replied: Whoever has two or more wives must treat them 
    fairly. It is not permissible for him to single out one of his wives in any 
    way to the exclusion of the other(s) with regard to spending, accommodation 
    and spending time with them. There is a stern warning issued to the one who 
    has two wives and does not treat them equally. It was narrated that Abu 
    Hurayrah (may Allaah be pleased with him) said: The Messenger of Allaah  
    (peace and blessings of Allaah be upon him) said: “Whoever has two wives and 
    favours one of them over the other will come on the Day of Resurrection with 
    half of his body leaning.” Narrated by Imam Ahmad in al-Musnad 
    (2/295, 347, 471). Al-Nasaa’i and Ibn Maajah narrated something similar in 
    their Sunans.

    It was narrated from Abu Hurayrah (may Allaah be pleased with 
    him) that the Prophet  (peace and blessings of Allaah be upon him) said: 
    “Whoever has two wives and inclines more towards one of them will come on 
    the Day of Resurrection with half his body leaning.” Narrated by Abu Dawood 
    in his Sunan (2/601). Al-Tirmidhi narrated a similar report in his 
    Jaami’. 

    This evidence indicates that it is essential to treat 
    co-wives fairly and that it is haraam for the husband to favour one of them 
    more than the other, apart from the inclination of the heart, for the 
    inclination of the heart cannot be controlled. Hence the Messenger of Allaah 
     (peace and blessings of Allaah be upon him) used to say: “O Allaah, 
    this is my division in that over which I have control, so do not call me to 
    account for that over which I have no control” (i.e., the love of the 
    heart). 

    Based on that, it is not permissible for this husband to give 
    things that he owns to one wife and not to the other. If he gives a house 
    etc to one of his wives then he must treat all his wives equally and also 
    give the same to all of his wives, or something of equal value, unless the 
    second wife lets him off. End quote from Fataawa al-Lajnah al-Daa’imah 
    (16/189). 

    And Allaah knows best.