Her parents are refusing to have an Islamic celebration; what should she do?

Firstly: 

What is meant by an Islamic celebration is a party that is
held in accordance with Islamic guidelines, so that it is free of the evils
of mixing and women showing their adornments in front of men, and using
music and immoral singing, and other things that Allaah has forbidden. These
haraam things, unfortunately, are widespread in many Muslim celebrations
nowadays, except for those on whom Allaah has mercy. What is prescribed with
regard to wedding parties is to bring joy and happiness to both bride and
groom and their families and those who come to congratulate them in ways
that do not incur the wrath of Allaah, such as using the duff (a kind of
hand drum) among women, and their singing for one another using words that
carry beneficial meanings and are free of sin. Al-Bukhaari (5163) narrated
from ‘Aa’ishah (may Allaah be pleased with her) that she presented a woman
as a bride to an Ansaari man, and the Prophet (peace and blessings of
Allaah be upon him) said to her: “O ‘Aa’ishah, did not have any
entertainment? For the Ansaar are fond of entertainment.” 

Ibn Majaah (1900) narrated that Ibn ‘Abbaas (may Allaah be
pleased with him) said: ‘Aa’ishah arranged a marriage for a female relative
of hers among the Ansaar, and the Messenger of Allaah (peace and
blessings of Allaah be upon him) came and said, “Have you taken the girl [to
her husband’s house]?” They said, Yes. He said, “Have you sent someone with
her to sing?” She said, No. The Messenger of Allaah (peace and
blessings of Allaah be upon him) said, “The Ansaar are people with romantic
feelings. Why don’t you send someone with her to say, ‘We have come to you,
we have come to you, may Allaah bless you and us’?” This hadeeth was classed
as hasan by al-Albaani in Irwa’ al-Ghaleel (1995). 

Al-Nasaa’i (3369) and Ibn Majaah (1896) narrated that
Muhammad ibn Haatib said: The Messenger of Allaah (peace and blessings
of Allaah be upon him) said: “What differentiates between haraam and halaal
is (beating) the daff and raising the voices (in song) at the time of
marriage.” Classed as hasan by al-Albaani in Saheeh al-Tirmidhi. 

Wedding parties in Islam are parties which combine bringing
of joy and happiness to those present with modesty, dignity and avoidance of
haraam things. 

Women should celebrate the wedding separately from men, and
do what is appropriate to them to bring happiness to the wife and the people
around her, such as providing entertainment, telling jokes and singing to
the accompaniment of the duff, and eating and drinking, and doing other
things that may vary according to customs and traditions, so long as it is
within the circle of permissibility. 

The same applies to the men; they should gather in a separate
place and exchange congratulations, and pray for blessing for the couple. It
is Sunnah for the husband to offer food to be eaten by those present,
without any extravagance. 

The aim behind wedding parties is to announce the marriage
and to make it distinct from haraam relationships, and to bring happiness to
the couple, their families and friends, whilst attaining true submission to
Allaah in all of that. 

Secondly: 

If the parents refuse to adhere to shar’i rulings in the
wedding party and they insist on including some evils, such as allowing
mixing or wanton display (tabarruj), or bringing a female singer or dancer
to perform in front of men, then you have to advise them, and explain the
shar’i ruling on such evils, and remind them that marriage is a blessing
from Allaah for which they should give thanks, and gratitude is to be shown
by obedience, not disobedience, and the marriage that begins with sin is
unlikely to be blessed. If they respond, then praise be to Allaah, but if
they persist in their view, then keep away from the place of evil [?] and
announce your dislike and disavowal of it. Allaah says (interpretation of
the meaning): 

“And it has already been revealed to you in the Book (this
Qur’aan) that when you hear the Verses of Allaah being denied and mocked at,
then sit not with them, until they engage in a talk other than that; (but if
you stayed with them) certainly in that case you would be like them. Surely,
Allaah will collect the hypocrites and disbelievers all together in Hell”

[al-Nisa’ 4:140] 

al-Qurtubi (may Allaah have mercy on him) said: This
indicates that it is obligatory to avoid people who commit sin if they do
any evil action openly, because the one who does not avoid them is approving
of their action. Allaah says “certainly in that case you would be like
them”, so everyone who sits in a gathering where sin is committed and
does not denounce it will share an equal burden of sin with them. 

He should denounce them if they speak of sin or do it; if he
is not able to denounce them then he should leave them so that he will not
be one of the people mentioned in this verse. End quote. 

The Prophet (peace and blessings of Allaah be upon him)
said: “Whoever among you sees an evil action, let him change it with his
hand (by taking action); if he cannot, then with his tongue (by speaking
out); and if he cannot, then with his heart (by hating it and feeling it is
wrong), and that is the weakest of faith.” Narrated by Muslim (49).  

For more information please see the answers to questions no.
11446 and
7577. 

You do not have to agree to the evil, or give up your stance
of adhering to the rulings of sharee’ah in weddings and otherwise, in order
to be among the victors who are blessed in this world and in the Hereafter.
 

We ask Allaah to guide you. 

And Allaah knows best.