No. Hyundai is its own company. Hyundai owns KIA. Chrysler, owned by Fiat Chrysler Corporation, is another separate company that currently only owns Dodge and Jeep, and previously owned Plymouth, Eagle, and Desoto. Hyundai is not part of Chrysler.
Chrysler who owns the Jeep brand merged with Daimler-Benz in 1998. Mercedes sold their interest in Chrysler and Jeep in 2007. Chrysler & Jeep are now partially owned Fiat. The company is called Chrysler LLC.
The Chrysler Corporation. MoPar is the term used for all Chrysler production parts as in Motor Parts. Over the years it has come to be related in any vehicle manufactured by Chrysler, Dodge, Desoto and Plymouth.