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Giving a wedding party and inviting people to express joy and announce the marriage, is something that is extra and recommended with regard to marriage, but it is not one of the conditions or essentials.
The Prophet (blessings and peace of Allah be upon him) said: “Proclaim the marriage.” Narrated by Ahmad (15697); classed as hasan by al-Albaani.
Al-Munaawi said: What is meant by proclaiming it is broadcasting news of it among the people.
End quote from Fayd al-Qadeer, 2/14
Ibn Qudaamah said: It is mustahabb to announce the marriage and bang the daff (hand drum) for it… so that it will become well known and recognized.
End quote from al-Mughni, 9/467
Holding a wedding party is one of the most common ways of announcing the marriage.
There is no doubt that your mother’s request to have a wedding party is the desire of every mother who loves to express joy and celebrate her daughter’s wedding, as well as taking into account people’s traditions and culture.
So at least have a small party, even if it is limited to the family, at reasonable cost and avoiding extravagance and wasting money. This will please your mother and will also achieve the purpose of announcing and proclaiming the marriage.
If you cannot do that, there is nothing wrong with you going to live with your husband even if you do not have a wedding party, because the marriage contract is complete and valid so long as it is done with the consent of both spouses and the woman’s guardian, and in the presence of witnesses.
See also the answer to question no. 2127
And Allah knows best.