Few indisputable facts which none of these Qisa-Go Maulanas and Zakirs, Allamas will narrate.
Hussain Pak RA did agree to give his hand in Yazeeds hand to do Bayt as part of his 3 terms to avoid a fight in Karbala. Saying he refused to do that till death is a lie.
ZainulAbideen did bayt in Yazeeds hands and accepted his Khilafat in Damascus. He was returned with lots of gifts and honor along with protection of soldiers to Madeena where he spent his life after.
Zainul Abideen never claimed to be Khalifa or successor during Yazeeds life and after his death as well nor he made any efforts to achieve that.
Most of Banu Umayyads took refuge in Zainul Abideen house when they were attacked on by people of Madeena during their rebellion against Yazeed.
First lady who did Matam e Hussain was Yazeeds Wife who was x wife of Hussain pak RA.
There more facts to narrate but Allamas n Zakir including Tariq Jameel only love to narrate what suits the emotions of public and appeals the masses.