When in doubt...

...Call a professional!
This bentwood rocker was brought in this week. The cane on the seat is pretty new and should have a lot more life left in it. However, when it was last replaced the old cane and spline was removed with a router power tool - a BIG no-no. Sheet cane removal should always be done with non-invasive hand tools to protect the wood and insure longevity of the furniture. It takes a lot more time and labor, but it is a step that should never be skipped. The router weakened the inside rim of the seat and when it was used 3/4 of the structure split apart. There was also very little glue holding the spline and cane in.

UPDATE:
Here is the finished restoration including gluing the seat back together and installing brand new sheet cane: