I read a story where Odin gave all his possessions to his brother Villi and Ve and made them the rulers of the Universe. One of Odin's possessions is his wife, Frigg. Hence, while Odin is away, his brothers "took possession" of Frigg. How true is this myth and why did Frigg, a goddess of marriage, willing go to her brothers in law?
Well, your telling is pretty distorted, but there is a story of Odin's brothers taking possession of his wife, Frigg. From the Ynglinga Saga, Chapter 3:
Odin had two brothers, the one called Ve, the other Vilje, and
they governed the kingdom when he was absent. It happened once
when Odin had gone to a great distance, and had been so long away
that the people Of Asia doubted if he would ever return home,
that his two brothers took it upon themselves to divide his
estate; but both of them took his wife Frigg to themselves. Odin
soon after returned home, and took his wife back.
Note, however, that no statement is made villifying Ve and Vilje, accusing them of violating Frigg or of them cuckolding Odin, nor is any mention made of reprisals for their transgressions. Odin simply returns, and takes his wife back.
Rather than a story of bad behavior, this seems to be a model for right behavior. If a man is lost, it may fall to their brother to take possession of their widow, as their own wife or mistress, and see to her care.
In fact, sometimes immediately after the death of their husbands, Icelandic women became the wives of relatives-in-law through inheritance; this came about, as a rule, through a man's falling heir to a deceased brother's widow along with his movable goods and this land. And even at present day in Scandinavia it is very customary for a man to marry the wife or betrothed of his brother, in the event of the latter's death.
Social Scandinavia in the Viking Age by Mary Wilhelmine Williams, page 104
So, to answer the title question directly "Did Frigg cheat?" No, she did not.