What is the best way to share custody if parents live on different coasts?

Shared but unequal. Equality and fairness is not the goal. The best interest of the children must be the guiding principle. With that, the parents can work out the details, such as where kids should live, go to school, and vacation. Geographic distance makes travel more challenging. However, the fundamental challenges remain the same. Child rearing requires coordination between parents. Divorce does not change this.
Bi-Coastal Custody. This is as much a legal question as a medical one. Custody laws vary from state to state. Also time spent with each parent may vary depending upon the age of the child. The most important this is for both parents to dialogue and keep the best interest of the child foremost. Your local area may also have family court mediators that can facilitate the dialogue. Best wishes!