All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
What you ordered your children to say is substantiated with evidence from the Sharee’ah and we hope that you will be rewarded for this –Allah willing.
Indeed, exalting mention of the Prophet is one of the best types of Athkaar (remembrances and supplications).
Verily, there are some Ahadeeth about exalting the mention of the Prophet ten times in the morning and ten times in the evening.
Abu Ad-Dardaa’ narrated that the Prophet said: “Whoever exalts my mention ten times in the morning (i.e. after Fajr) and ten times in the early evening (i.e. after 'Asr), he will receive my intercession on the Day of Judgment.” [At-Tabaraani]
The scholars differed in opinion about the classification of this Hadeeth; some classified it as Dha’eef (inauthentic) and some classified it as authentic.
Al-Haythami said in his book Al-Mujama’: “At-Tabaraani reported it with two chains of narrators; one of which is good and its men are considered as trustworthy.” [End of quote]
The Hadeeth was also classified as Hassan by Al-Albaani in his book Saheeh Al-Jaami’ (no 6357), but he then changed his opinion and classified it as Dha’eef in Dha’eef At-Targheeb wat-Tarheeb (no 396), and in As-Silsilah Adh-Dha’eefah, no 5788.
Prior to him, Al-'Iraqi classified this Hadeeth as Dha’eef as he said in Takhreej Al-Ihyaa’: “There is an interruption in it (i.e., in its chain of narrators).” [End of quote]
As-Sakhaawi also said the same thing in Al-Qawl Al-Badee’: “There is an interruption in this Hadeeth because Khaalid [one of the narrators] did not hear from Abu Ad-Dardaa'; it was also reported by Abu ‘Aasim and it is inauthentic.” [End of quote]
However, we do not see any harm in acting according to this Hadeeth even if it is Dha’eef , because it is not very Dha’eef, and what is mentioned in it is included in other authentic Ahadeeth that encourage people to exalt the mention of the Prophet .
Ibn Muflih from the Hanbali School of jurisprudence said in Al-Aadaab Ash-Shar’iyyah:
“It was confirmed by many scholars who authored books on the sciences of Hadeeth, and who quoted from the early scholars, that we can act according to a Dha’eef Hadeeth in matters that do not involve Tahleel (making things lawful) or Tahreem (making things forbidden), such as in acts of virtues; the same opinion was reported from Imam Ahmad.”
The Fatwa of Shihaab Ad-Deen Ar-Ramli, from the Shaafi'i School of jurisprudence, about acting upon a Dha’eef Hadeeth and whether or not a ruling can be confirmed with it reads:
“An-Nawawi reported, in many of his books, the consensus of the scholars of Hadeeth that a Dha’eef Hadeeth is acted upon in acts of virtue and the like, especially that Ibn ‘Abdul-Barr said that the Ahadeeth of virtues are acted upon, and Al-Haakim said: I heard Abu Zakariyyah Al-‘Anbari saying that if the Hadeeth does not forbid what is lawful, and does not make permissible what is forbidden, and does not make something an obligation, and it includes encouraging people to do good and warning people from evil, then we turn a blind eye to it (i.e., its classification) and it is reported without any objection.”
Allah knows best.