"appropriate relationship" is a complete misnomer - every couple is different.
Sharing your wife is more than just widening your sexual experiences. It also helps in building trust.
Many men and women are involved in infidelity or unfaithfulness simply because their marriage life sucks. Unfaithfulness brings mistrust in a marriage. Nonetheless, Wife sharing allows the husband and wife to experiment with other people openly. The openness and transparency builds trust among the couples. In fact, A couple will not engage in other affairs without first informing his/her partner.
No, I don't think that wife sharing has a positive influence on family life. While I'm okay to a point with any alternative family relationship, I still think that the best way to raise a child is with just 2 or 1 parents. And those parents must have clearly definable relationships to the child.
To enter into a marriage is a solemn vow. Breaking that vow is either a sin against your God or your partner. Either way, you are breaking a promise. Integrity is one of the few things in this world that is exclusive to humans, and we betray it all too often. It is better to divorce and carry on in such ways. Accept that you could not keep your promise and make a declaration that reflects that.
I do not believe wife-sharing has a positive influence on family life. I believe it can set the foundation for youth to have the wrong ideas about appropriate relationships or what is common in normal society. Wife-sharing is not common so exposing it to children could cause problems for them in adulthood. Thus, it doesn't postively influence family life.
While every family is different and needs to make decisions based on it's own individual needs, the practice of wife-sharing is sure to cause major difficulties in the average family. While wife-sharing may be intriguing to some, issues such as jealousy and extra-marital pregnancies are sure to arise and create a rift in not only the relationship but also possibly with any children in the household.
I don't believe that an open marriage, such as sharing a wife among multiple men, would be a positive thing for family structure. There would potentially be mistrust in this type of open marriage, with people not really being fully devoted to one another. Similarly with polygamy when there is husband-sharing, it also creates an issue with there being too many of one gender. Some sects have had issues with there being too many males when the men have multiple wives.