Answer
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.
In this fatwa:
1- It is permissible for a Muslim to accept gifts from non-Muslim parents.
2- There is no harm if you are appointed the alternate trustee for your parents’ estate since it is valid for a non-Muslim to appoint a Muslim as a guardian over his property.
Answering your question, Dar Al-Ifta Al-Misriyyah, states:
Accepting gifts from non-Muslims
It is permissible for a Muslim to accept gifts from a non-Muslim. God Almighty has permitted benevolence and justice toward non-Muslims who do not fight Muslims. He says; {God forbids you not, with regard to those who fight you not for (your) faith nor drive you out of your homes, from dealing kindly and justly with them: For God loves those who are just.} (Al-Mumtahanah 60:8)
Abu Humaid al-Sa’di (may God be pleased with him) said:
“We went on the conquest of Tabuk with the Prophet (peace and blessings be upon him). The king of ‘Aela gave him a white mule and a cloak as a gift” (Al-Bukhari and Muslim)
There is no harm if you are appointed the alternate trustee for your parents’ estate since it is valid for a non-Muslim to appoint a Muslim as a guardian over his property.
Imam An-Nawawi said:
“It is not permissible for a Muslim to appoint a non-Muslim as a guardian over his property though the opposite is valid.”
Al-Khatib al-Shirbini said:
“Scholars are in agreement that it is valid for a dhimmi (non-Muslim living under Muslim rule) to appoint a Muslim as a guardian over his property and it is permissible for a Muslim to testify against a dhimmi. It was established that it is permissible for a Muslim to act as a guardian over the property of a dhimmi as the imam may act as the guardian of a dhimmi female in the matter of her marriage” (Mughni Al-Muhtaj, 3/74)
Almighty Allah knows best.
Source: Dar al-Ifta al-Misriyyah