All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
The Hadeeth which you mentioned in the question is graded as Dha’eef [weak] by the scholars, like Ibn Katheer in his Tafseer [interpretation of the Quran] and also in his book entitled "Al-Fusool Fi Ikhtisaar Seerat Ar-Rasool”. Shaykh Al-Albaani also graded it as Dha’eef when he classified the Ahaadeeth reported by An-Nassaa’i in his Sunan.
Besides, Shaykh Ibn Taymiyyah said in his interpretation of Chapter 112 of the Quran: “The Prophet did not pray that night except in Al-Aqsa Mosque as confirmed in the Saheeh (sound) narrations and he absolutely did not stop except at it.”
Shaykh Ibn Taymiyyah graded this narration [which is mentioned in the question] as fabricated. He wrote in his book entitled Iqtidhaa’ As-Siraat Al-Mustaqeem: “…and it includes what is fabricated such as what was reported by some narrators that the Prophet was told by Jibreel (Gabriel) : “This is the grave of your father Ibraaheem (Abraham), so get off (form the Buraaq) and pray at it, and this is Bethlehem, the birthplace of your brother ‘Eesa (Jesus), so get off and pray in it.”
Moreover, Ibn Al-Qayyim said in his book entitled Zaad Al-Ma’aad: “It was said that he – i.e. the Prophet - stopped at Bethlehem and prayed in it but this is not authentic from him at all.”
Therefore, this Hadeeth is not authentic at all. For more benefit on the beliefs of the Brelwi sect, please refer to Fatwa 87790.
Allaah Knows best.