My question is: what is the distant to have two Friday prayer in a Muslim village according to Islam. There is one mosque which has enough space for the village crowd. Despite this can have two Friday prayer? Can you explain this with proofs of Hadeeth?

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 is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

We are not aware of any evidence in Islam that specifies a given distance between mosques in the same area that makes it lawful to pray more than one Jumu'ah.

What is proved is that during the era of the Prophet there was only one mosque in Madeenah where Jumu'ah is performed.  This situation continued during the era of the Caliphs.  This is considered evidence from the actions of the Prophet that he deliberately gathered the people living in the same area in one mosque behind a single Imaam.

On the other hand, if the distance between the two mosques is so far that it becomes hard for people to pray in one mosque or if the mosque in which Jumu'ah is performed is too small to accommodate the number of people who pray in it and if there are no empty areas adjacent to it or courtyards, then there is no objection to performing Jumu'ah in other mosques in the same area according to the necessity in order to make matters easy for people to perform their duties without hardship.  Allaah Says (which means): {And strive for Allaah with the striving due to Him. He has chosen you and has not placed upon you in the religion any difficulty. [It is] the religion of your father, Abraham. He [i.e. Allaah] named you Muslims before [in former scriptures] and in this [revelation] that the Messenger may be a witness over you and you may be witnesses over the people. So establish prayer and give Zakah and hold fast to Allaah. He is your protector; and excellent is the protector, and excellent is the helper.}[Quran 22:78]. Allaah also Says (which means): {The month of Ramadan [is that] in which was revealed the Quran, a guidance for the people and clear proofs of guidance and criterion. So whoever sights [the new moon of] the month, let him fast it; and whoever is ill or on a journey- then an equal number of other days. Allaah intends for you ease and does not intend for you hardship and [wants] for you to complete the period and to glorify Allaah for that [to] which He has guided you; and perhaps you will be grateful.}[Quran 2:185].

This is why when Muslims become numerous and mosques can no longer accommodate them, they started praying Jumu'ah in more than one mosque in the same town based on evidence related to the principle of easiness and eliminating hardship.  As for praying Jumu'ah in more than one place in the same area for no reason, it is unlawful according to the majority of Muslim scholars.  Had it been lawful, the Prophet would have told his companions to pray Jumu'ah in their different mosques in the suburbs of Madeenah because he was known to choose the easiest between any two options.