Answer
Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear sister in Islam, we commend your pursuit of knowledge and your eagerness to seek what is lawful and avoid what is not. We earnestly implore Allah to bless your efforts in this honorable way.
It goes without saying that Islam commands us to establish good relations with our relatives and neighbors whether they are Muslims or not. As Muslims, we should do our best to be good to them and to become close to them, as this will bring them closer to Islam. However, a Muslim must refrain from participating in any act that violates Islamic teachings.
Therefore, there is nothing wrong as far as Islam is concerned if you and your family attend your cousin’s wedding ceremony as long as you do not participate in any specific religious rituals that they may perform. Moreover, there is nothing wrong in acting as a flower girl, for it does not have any specific religious connotations.
In his response to the question you raised, Sheikh Ahmad Kutty, a senior lecturer and an Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states:
There is nothing wrong in Islam for you and your family to attend the Christian marriage ceremony. Islam teaches us to be kind and reciprocate kindness with our neighbors and fellow human beings.
Accordingly, we are encouraged to deal with them on humane terms so long as we do not commit actions that are condemned by Allah and His Messenger. By attending the marriage, you are only establishing good relations, which is a neighborly duty that we Muslims are enjoined to fulfill.
Good neighborliness is a prescribed Islamic duty that has been heavily stressed in the Qur’an and the Prophetic traditions. Therefore, you may go ahead and participate in their wedding and demonstrate the noble teachings of Islam.
While doing so, however, you should not participate in any specific religious rituals that they may perform, which may contain elements of shirk or associating other partners with Allah.
Acting as a flower girl does not fall in this category, as it is simply a custom in many cultures, and as such it does not have any specific religious connotations. So, we should not have any inhibitions in participating in such customs.
Allah Almighty knows best.