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

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.