This is a shighaar (quid pro quo) marriage and is not permissible

 

I am a young man and I did the marriage contract with my cousin (the daughter of my maternal aunt), but I do not love her, I love her sister. But I was forced into that because her brother would not marry my sister unless I married the one whom I do not love. The girl knows that I cannot stand her, but her family insisted that she marry me. Now I do not know what I should do.

Praise be to Allaah.

Allaah has honoured man with reason and He has given him free
will to choose that to which his religion, reason and character make him
inclined, so that he may rise above the promptings of whims and desires and
of the shaytaan. So the one who has been honoured in this way should not be
heedless and respond to the desires of those who are around him and their
hateful customs.  

In the Sunnah there is a prohibition on the kind of marriage
that you have entered into, which is called nikaah al-shighaar (quid pro quo
marriage). 

It was narrated from Ibn ‘Umar (may Allaah be pleased with
him) that the Messenger of Allaah (peace and blessings of Allaah be
upon him) forbade shighaar. Narrated by al-Bukhaari (5112) and Muslim
(1415). 

A shighaar (quid pro quo) marriage is when it is stipulated
that each man will marry the daughter, sister or ward of the other, whether
there is any mahr or not. 

It says in al-Mudawwanah (2/98): 

What do you think if someone says “Marry your daughter to me
for one hundred dinars on the basis that I will marry my daughter to you for
one hundred dinars”? Malik disliked that and regarded it as a kind of
shighaar. 

This is also indicated by the report narrated by Abu Dawood
(2075) and others from ‘Abd al-Rahmaan ibn Hormuz, that al-‘Abbaas ibn
‘Abd-Allaah ibn ‘Abbaas gave his daughter in marriage to ‘Abd al-Rahmaan ibn
al-Hakam, and ‘Abd al-Rahmaan gave his daughter in marriage to him, and they
both gave dowries. Mu’aawiyah ibn Abi Sufyaan wrote to Marwaan ibn al-Hakam
telling him to separate them, and he said in his letter: This is shighaar
which was forbidden by the Messenger of Allaah (peace and blessings of
Allaah be upon him). 

Some of the scholars regarded shighaar as an invalid marriage
which cannot be gone ahead with. 

It says in Fataawa al-Lajnah al-Daa’imah (18/427): 

If a man gives his ward in marriage to a man on the basis
that the other will give his ward to him in marriage, this is the shighaar
marriage which was forbidden by the Prophet (peace and blessings of
Allaah be upon him). This is what some people call an “exchange” marriage,
and it is an invalid marriage, whether a dowry is given or not, and whether
there is mutual consent or not. 

But if one man proposes marriage to the ward of another man,
and the other proposes marriage to the ward of the first, without any
stipulation, and the marriages are done with the consent of both women and
all the other conditions of marriage are met, then there is no dispute
concerning that, and in that case it is not a shighaar marriage. End quote. 

See also the answer to question no.
11515. 

Thus it is clear that you have done something that is
forbidden in Islam as well as being reprehensible in social and
psychological terms. 

That is because marriage should start with consent and be
entered into by choice. Islam is keen to ensure the consent of both parties,
to such an extent that the Prophet (peace and blessings of Allaah be
upon him) said: “A virgin should not be married off until her permission has
been sought.” Narrated by al-Bukhaari (5136) and Muslim (1419). 

If marriage is not done with consent then it is usually
doomed to failure, so how about if the husband dislikes his wife as is the
case here? 

Even more serious than this is the fact that you love the
sister of the one with whom you have done the marriage contract. Your
dislike of the one with whom you did the marriage contract and your love for
her sister means that your nafs (self) will call you to consider haraam
things, and the shaytaan will find a great opportunity to make sin appealing
to you. It will also deprive you of happiness in your marriage and
contentment and love between you and your wife. 

The reason for that is going against the laws of Allaah and
entering into a shighaar marriage. 

Our advice to you is not to go ahead with this marriage and
not to respond to any attempt to make excuses. You should explain to your
sister’s husband that connecting one marriage contract to the other is
haraam, and renders both contracts invalid. He should keep his wife, but at
the same time he should do the marriage contract again, because the contract
is invalid due to the shighaar. If he refuses and insists on leaving her,
then Allaah says (interpretation of the meaning): 

“But if they separate
(by divorce), Allaah will provide abundance for everyone of them from His
Bounty. And Allaah is Ever All‑Sufficient for His creatures’ needs, All‑Wise”

[al-Nisa’ 4:130] 

I remind you to fear Allaah and urge you not to transgress
His sacred limits by trying to get in touch with that girl whom you love. If
you cannot marry her in a proper manner, then you have to cut off all ties
with her completely. 

We ask Allaah to guide you. 

And Allaah knows best.