I pray to Allah to console your heart, inspire you with patience in accepting the will of Allah, and forgive your beloved mother.
As for the wish of your mom for you to lead her funeral prayer, there is no need for you to brood over it now. You only came to know about it later. Since funeral prayer is already done, it is not necessary to redo it.
However, if there are people who did not attend the funeral prayer and they want to do it, you may accompany them to the graveyard, and you may lead them in prayer.
Otherwise, you need not feel guilty over this mistake on your part. It was not intentional on your part. The Prophet (peace be upon him) said, "Allah has excused the members of my community for their wilful mistakes, forgetfulness, and slip-ups."