Sheri,

You just need to pick up the phone and plan on staying on it for at least an hour. Every airline and alliance is different. I'd do some leg work yourself first and look at possible routes. Sometimes you get a good res agent who can figure it out, sometimes they simply say what their computer screen tells them. You may need to allow some flexibility, use multiple stops or an overnight to get the availability or class of service.

For UA both the outbound and return need to be available for booking, while AA will let you hold outbound until the return is available (within a certain window).

There are even different rules within alliances, depending on the airline. There is no easy answer. It takes time, flexibility and patience. The more status you have, you may get a more senior Res agent.