Secondly if Eid falls on Friday than I am sure there should not be a problem to pray Jumuah as they are both Eids, though one marks the end of Ramdhan and the other is weekly and both have their own merits. According to my research, there is difference of opinion, it can be prayed if people wish to. The situation at the time of the Prophet was that people had to travel long distance to get the Masjid so they were allowed not to pray Jumuah, instead pray Zohar salat.
بسم الله الرحمن الرحيم
The Hadith of Salat al-Tasbeeh was narrated from more than ten Sahaba (رضی اللہ عنھم) and the sanad of some of these traditions is undoubtedly Sahih or Hasan according to the majority of Muhaddithin (scholars of Hadith). Therefore, this salah is proved from the Prophet (صلی اللہ علیہ وسلم) and it is never an invention of the Ulama. The ghair muqallid who denies it is extremely ignorant of the Quran and Hadith. You should ask him to study Maarifus Sunan (4/282-289) and the sources mentioned therein and then decide justly fearing Allah Almighty whether this salah is proved from the Prophet (صلی اللہ علیہ وسلم) or an invention of Ulama. He should not follow someone blindly leaving the academic research and opinion of majority of Ulama.
Allah knows Best!
Darul Uloom Deoband