Praise be to Allah.
Can a child lead prayer?
It is OK for a boy who understands the prayer to lead others in prayer, because the Prophet (peace and blessings of Allah be upon him) said: “People should be led in prayer by the one who knows the most Quran among them.” (Narrated by Muslim, al-Masajid wa Mawadi’ al-Salah, 1078)
It was narrated in Sahih al-Bukhari that ‘Amr ibn Salamah al-Jarami said: “My father came from the Prophet (peace and blessings of Allah be upon him) and said that he had heard the Prophet (peace and blessings of Allah be upon him) say, ‘When the time for prayer comes, let the one among you who knows the most Quran lead you in prayer.’ They looked and they did not find anyone who knew more Quran than me, so they made me lead them in prayer, and I was a boy of six or seven years.” (Al-Maghazi, 3963. See Fatawa al-Lajnah al-Daimah, 7/389-390)
The evidence to be found in the hadith is that these Companions asked ‘Amr ibn Salamah to lead them in prayer when he was six or seven years old. This indicates that a boy who has reached the age of discernment can lead the prayers. If that were not permitted, there would have been Revelation to say that it was not allowed. (Ahkam al-Imamah wa’l-I-itimam fi’l-Salah by ‘Abd al-Muhsin al-Munif).
If your son fulfils all the conditions and obligations of the prayer, then there is nothing wrong with him leading you.
Can a mother lead her son in prayer?
With regard to a woman leading a boy in prayer , this is not permissible, because he comes under the same rulings as a man. What is permitted is for a woman to lead other women in prayer , because the Prophet (peace and blessings of Allah be upon him) commanded Umm Waraqah bint ‘Abd-Allah ibn Nawfal to lead the members of her household – i.e., the women – in prayer. (Narrated by Abu Dawud, al-Salah, Imamat al-Nisa, 500, Classed as sahih by al-Albani in Sahih Sunan Abi Dawud, 553)
And Allah knows best.