From you description it sounds like you have a cesspool and a seepage pit. A cesspool is a pit without a septic tank in front of it. It therefore get all of the sewage and grease. These pits need to be cleaned about once a year in order to remove the sludge and help keep the water flowing. Your first pit will be used until it fills and fails, and then the second pit will get all of the water until it fails.

You do not indicate how old the system is. The best approach is probably to have the first pit pumped and treated. Then ensure a baffle in placed on the connecting pipe between the two pits to reduce the sludge and grease that flows between them. This will help make the first pit a pseudo septic tank and when it fill, the second a true seepage pit. After treating the first pit, the second will recover somewhat while the first pit fills again. If it does not recover enough, the it may also need to be treated. 

If you are going to have this type of work done, be sure to install access to these pits for easier treatment in the future.

If you would like to discuss further, please do not hesitate to call.