They did not carry out their father’s last wishes, and the ruling on doing Hajj before execution of the will
Question

 
My wife’s father died and left behind three sons and four daughters; he also left behind real estate worth 100 million, and he left behind instructions to his heirs that the value of his estate should be given in charity for a water or mosque project. But the heirs did not acknowledge the will, despite the fact that the will was written and witnessed by two witnesses, but it was not officially recorded in the court.
Now my wife wants to go for Hajj. Is it permissible for her to do Hajj using the money that she inherited from her father, when she did not carry out his last wishes? Is this regarded as a debt that she owes, and is there any sin on her?
Praise be to Allah.If a person dies and leaves behind wealth, what his heirs must do is start by preparing him and shrouding him, (paying for that) from the estate. Then after that, they must pay any debts owed, then give any bequests from one third of the estate. All of that must be done before dividing the estate. Allah, may He be exalted, has instructed His slaves to divide estates in accordance with what He has prescribed for them, but that must be done after carrying out any bequests. Allah may He be exalted, says (interpretation of the meaning): “(The distribution in all cases is) after the payment of legacies he may have bequeathed or debts” [an-Nisa’ 4:11]. 
Al-Qurtubi said in his Tafseer (5/61): There is no inheritance except after payment of debts and bequests. If a person dies, some certain dues that he owes are to be paid from his estate, then whatever is required to shroud and bury him, then debts are to be paid in the order in which they are due., Then bequests are to be paid from the one third, and similar payments also in order, then the remainder is an inheritance to be shared among the heirs. End quote. 
Debts take precedence over bequests. Ibn Katheer (may Allah have mercy on him) said in his Tafseer (2/201): Debts take precedence over bequests; after that come bequests, then inheritance. This is a matter on which there is scholarly consensus. End quote. 
In order for it to be obligatory for this bequest to be executed, it is not stipulated that it should have been documented in the court or recorded with any specialist department, or have been witnessed by witnesses, or to have been written down. Rather if the heir is aware of this bequest – either because he heard it directly from the owner of the wealth or in any other manner – then he is obliged to execute it, even if there is no shar‘i proof concerning which the shar‘i judges may pass a verdict in the event of any dispute. 
Based on that, what the heirs must do is fulfil their father’s bequest. If they refuse to fulfil his bequest, then those among them who refused to carry out the legitimate bequest have sinned, and whatever of that bequest has been added to their wealth is haraam and is not permissible for them. Allah, may He be exalted, says, warning the one who does that (interpretation of the meaning): “Then whoever changes the bequest after hearing it, the sin shall be on those who make the change. Truly, Allah is All-Hearer, All-Knower” [al-Baqarah 2:181]. 
Ash-Shawkaani (may Allah have mercy on him) said: Changing means altering. This is a warning to the one who changes a bequest that is proper, in which there is no unfairness or harm. He carries the burden of sin, and there is no blame on the one who made that bequest; he discharged his duty by making that bequest.
End quote from Fath al-Qadeer (1/231) 
Secondly: 
The portion of your wife’s wealth from the estate that is haraam is the portion that was included in her share of this bequest. If they divided the estate among themselves in accordance with the shares allocated by sharee‘ah, then the value of her share from this bequest is the portion that she must get rid of by donating it to the causes singled out by her father for the bequest. If the other heirs respond to that, and give from their wealth what they are obliged to give, then this is the desired outcome. Otherwise she must dispose of what she is obliged to give from her wealth, and she should not care what the others do. 
Imam an-Nawawi (may Allah have mercy on him) said: If a person has decided to travel for Hajj or on campaign or any other purpose, then he should start by repenting from all sins and reprehensible actions, and he should settle any issue involving wrongdoing that he may have done to people, pay off whatever he can of debts to them, return anything that has been entrusted to him, and seek pardon from anyone with whom he has any dealings or whom he accompanied; he should also write his will and have it witnessed, and he should appoint someone who will be able to pay off his debts; he should leave for his family whatever he needs to cover their expenses until he returns.
End quote from al-Majmoo‘ (4/265) 
Thirdly: 
If the heirs or some of them did Hajj before executing the will of the deceased, then if the amount that must be spent on the bequest is specified, and Hajj was done from that money, which was unlawful to them, the Hajj is still valid, according to the more correct of the two scholarly views, but there remains the sin of usurping wealth and consuming something prohibited. 
But if the Hajj was not done with the money that was taken from the bequest unlawfully, and it was done with other funds or the haraam money was mixed with other, permissible money, then it is more appropriate to say that the Hajj is valid, and the validity of Hajj is unconnected to the issue of usurping the wealth. 
Hence the scholars (may Allah have mercy on them) said: If a person does Hajj using haraam wealth, such as that which has been usurped or stolen, his Hajj is valid. 
For more information, please see the answer to question no. 48986 
Whatever the case, what you must do is instruct your wife to return what she owes of this money to his family, because she cannot discharge her duty except by doing that, regardless of whether or not she has done Hajj. If she wants her Hajj to be accepted by Allah, then she must hasten to give back what she owes and return it to its rightful owners. 
And Allah knows best.