If you do not want the public to be privy to the details surrounding your divorce, the key thing is to keep it out of the courts, as the public has access to all discussions, evidence and outcome.
Unless there is abuse or bullying, or one party refuses to communicate with the other, there are alternatives to litigation.
The Harvard Law School Program on Negotiation discusses that mediation has become a popular option for couples willing to work together to come up with a fair divorce agreement. During a series of sessions, a mediator helps the two sides communicate about debt division, child custody, living arrangements and spousal support.
Not only does mediation save the couple time and money, but settlement rates are higher and of better quality. Couples are in control of the outcome, and they tend to communicate better after the divorce. Plus, all discussions are confidential.
Another option is collaborative law. FindLaw discusses that this combines both mediation and negotiation. Each party hires an attorney who does the negotiating. Each party should meet separately with their lawyer and be clear about what they want and what they are willing to negotiate. If the attorneys are unable to come up with an equitable agreement, and the parties decide to move on to litigation, they must hire new lawyers for the court battle.
In both collaborative law and mediation, each party is able to hire professionals, such as accountants, marriage therapists or child psychologists, to assist with more difficult topics. As with mediation, the discussions and decisions made in collaborative law are also confidential.