While an "amicable divorce" may seem like an oxymoron, it's still possible to reach a divorce settlement in a peaceful way. Divorce is often the result of two people failing to see eye to eye; although if those two people can agree on treating each other with civility and respect and are willing to be transparent in their marital finances and also both want the best for their children, there's hope of an amicable divorce.
An aggressive push for the best settlement possible, on the other hand, will likely be met with equal resistance; ill-will offered by one party met with equal ill-will, with both parties seeking to attribute fault and blame to the other. Once the divorce becomes "just another fight," it's a fight that may require a judge to order a resolution that might not be as advantageous as a negotiated settlement.
The alternative is to work together to discuss how your lives will play out after the divorce and the best ways to minimize the adverse consequences of what has become a difficult relationship. This becomes a challenge if two people are no longer on speaking terms, although there's no reason that a mutually beneficial resolution can't be achieved even in that context through attorneys or other representatives. In fact, it may take the assistance of other helpful professionals to help keep the process a constructive one.
Rather than just announce you are divorcing through having your soon-to-be-ex served with court papers, give some thought to discussing it together first. The petition that initiates the divorce process can feel aggressive if not anticipated, making it an aggressive and adversarial process from the beginning. Furthermore, focus on issues rather than haggling over positions. This will make it easier to work together to find solutions to issues rather than pushing and defending often irreconcilable positions.
This doesn't mean an amicable divorce is any less emotional. The difference is that the emotions are addressed separately and constructively, rather than ignored and used to fuel costly litigation.
If the purpose of divorce is to terminate a painful situation, you might question the value of prolonging that pain through court proceedings. An amicable divorce emphasizes the future, not the emotional issues that made living together unendurable. Divorce should be a chance for everyone to move on.