Is it permissible for a worshipper to lead his grandmother in prayer at home after performing the obligatory prayer in the mosque, especially in the Fajr and 'Asr prayers, after which there are no supererogatory prayers, with the intention that his prayer with her is supererogatory, in compliance with the Hadith of Mu'adh?

It is permissible for you to pray with your grandmother after you return from performing the obligatory prayer. Repeating the Fajr and Asr prayers with the intention of a supererogatory (nafila) prayer is permissible because it is for a legitimate reason, and prayers with specific reasons may be performed during times when prayer is otherwise prohibited. Your delay in the mosque does not prevent you from praying with your grandmother, as long as it does not result in the prayer going beyond its prescribed time.