How can I kill a very invasive rhubarb plant?
Are you certain that you have correctly identified the plant? Rhubarb is not at all invasive. It forms clumps that slowly spread in diameter, but don't get out of control.
Could the weed that you have possibly be burdock? The leaves of this plant look similar to rhubarb, but it develops prickly burs, which are the seeds by which it spreads. Burdock is a biennial, meaning that it grows vegetatively its first year, then flowers, forms seeds, and dies the second year. It has an extensive taproot, so to get rid of established plants, you need to dig it out. If you prevent it from forming burs, the number of new plants will eventually be reduced.