Did John Wesley use to pray in Latin due to the bad relationship with his wife?

While not covering John Wesley specifically, I should note that for a very long time mass was done in latin only, for Catholic Church, that was up to Second Vatican Council in the 1960s. As a result, some people would thus consider latin as the language to talk with God. And even if just whispering a Pater Noster, someone overhearing it might only pick that it was latin.

I'm not sure if the Book of Common Prayer would be in English at that time, it was probably in latin. However, even just looking at the Wikipedia article, we can see that from a young age «They were expected to become proficient in Latin and Greek and to have learned major portions of the New Testament by heart. Susanna Wesley examined each child before the midday meal and before evening prayers»

I also strongly suspect that his teaching at Christ Church College would be in latin. In any case, I think it is clear he was a fluent latin speaker.

While not having a reference for that, I don't find strange that he would use latin (remember, the language of intellectuals and in which knowledge was shared) to communicate with the Divinity.

That he prayed in latin so that his wife won't understand him I find more doubtful. Just like the idea that she would throw old shoes at his head everytime he prayed. It looks like an explanation that someone could have made up later, maybe something innocent like interpreting "At one time, he was at home praying in latin, and she threw him an old shoe" into "... he was praying in latin, so that she wouldn't understand it and she threw him an old shoe", or even the way an upset wife could present her point of view on their problematic marriage "I am sure he prays in latin on purpose so that I can't understand him!"

I answered this question before the OP changed it to John Wesley.

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I could find no mention of a wife in the various articles available on line regarding John Wycliffe (1320 - 1384). However there is an account of his being exhumed that his body might be desecrated (by being burned and his ashes scattered) and there is testimony to his unblemished character and his frugal way of life :

The Council of Constance declared Wycliffe (on May 4, 1415) a stiff-necked heretic and under the ban of the Church. It was decreed that his books be burned and his remains be exhumed. The latter did not happen till twelve years afterward, when at the command of Pope Martin V they were dug up, burned, and the ashes cast into the river Swift that flows through Lutterworth.

None of Wycliffe's contemporaries left a complete picture of his person, his life, and his activities. The pictures representing him are from a later period. One must be content with certain scattered expressions found in the history of the trial by William Thorpe (1407).

It appears that Wycliffe was spare of body, indeed of wasted appearance, and not strong physically. He was of unblemished walk in life, says Thorpe, and was regarded affectionately by people of rank, who often consorted with him, took down his sayings, and clung to him. "I indeed clove to none closer than to him, the wisest and most blessed of all men whom I have ever found. From him one could learn in truth what the Church of Christ is and how it should be ruled and led." Huss wished that his soul might be wherever that of Wycliffe was found.[8]

According to Philip Schaff: Wyclif was spare, and probably never of robust health, but he was not an ascetic. He was fond of a good meal. In temper he was quick, in mind clear, in moral character unblemished. Towards his enemies he was sharp, but never coarse or ribald. William Thorpe, a young contemporary standing in the court of Archbishop Arundel, bore testimony that "he was emaciated in body and well-nigh destitute of strength, and in conduct most innocent. Very many of the chief men of England conferred with him, loved him dearly, wrote down his sayings and followed his manner of life."[9]

New World Encyclopedia

(8) http://www.ccel.org/s/schaff/encyc/encyc12/htm/TOC.htm. Retrieved October 29, 2008.

(9) History of the Christian Church, Chapter V, Reformers before the Reformation, by Philip Schaff, http://www.ccel.org/s/schaff/history/6_ch05.htm. Retrieved October 29, 2008.

From the Wikipedia article on the subject:

Though Wesley favoured celibacy rather than marital bond, he married very unhappily at the age of 48 to a widow, Mary Vazeille, described as "a well-to-do widow and mother of four children." The couple had no children. Vazeille left him 15 years later. John Singleton writes:

"By 1758 she had left him – unable to cope, it is said, with the competition for his time and devotion presented by the ever-burgeoning Methodist movement. Molly, as she was known, was to return and leave him again on several occasions before their final separation."

Wesley wryly reported in his journal, "I did not forsake her, I did not dismiss her, I will not recall her."

What is the source of the idea that John Wesley used to pray in Latin so that his spouse won't understand?

Most likely from the author's personal sense of humor (the entire presentation seems to adopt a colloquial rather than scholarly tone); Latin basically served as an international and prestige language in much of the Western world until the late nineteenth and early twentieth century; it's highly unlikely that its usage in either individual prayer, private conversation, or public discourse, was done for the purpose of hiding anything from anyone; many Catholics, with which High Church Anglicanism is intimately connected (see Anglo-Catholicism), still serve Mass in Latin even today, let alone in Wesley's time.