Umar vs Ayesha on mourning the dead

With the advent of Muharram, arrives the false propaganda against mourning and weeping over the dead from the so called followers of true Islam.

While these Muslims disagree with the Shias on the point of whether to weep or not, let us see whether two of their very revered personalities, Umar and Ayesha had a common view on this issue.

It is narrated from Saeed b. Musayyab that Ayesha mourned over her father after his death. When this news reached Umar, he ordered prohibition against it, but Ayesha rejected the caliph’s order. Then Hesham b. Walid was ordered to go to Ayesha and stop her from mourning loudly. As soon as the women acted as per Hesham’s order, they left the house and Umar addressed them saying, ‘Do you intend to chastise Abu Bakr by your weeping? Surely the dead are chastised due to weeping over them.’

(Sahih Tirmizi: tradition 1002)

From the above incident it can be concluded that:
1. If the Prophet (s.a.w.a.) had actually prohibited weeping over the dead (as Umar claimed), then by crying, Ayesha disobeyed the Prophet’s (s.a.w.a.) order.

2. It can be argued that she must have been overcome by her emotions, but when Umar ordered her not to weep, she did not obey him thereby disobeying the so-called caliph of Muslims.

This makes Ayesha someone who
a. did not follow the Prophet’s (s.a.w.a.) tradition
b. was overcome by her emotions
c. disobeyed the so-called caliph

Yet, Bukhari has recorded many traditions from her in his Sahih.