I have tried Liquid Plummer and other drain clearing products, but the problem still exists. Our home is 10 years old and the tub has a metal stopper that I can't figure out how to remove so that I can use a snake. How do I remove the stopper and what (product) should I use to fix my problem? Thanks in advance.

Just get natriumhydroxide (NaOH) (= caustic soda) crystals.
Pour several liters of boiling water through the drain and wait till all water has disappeared.
Than drop a cup of caustic soda crystals in the drain, and flush away with a liter of boiling water.

Careful : there may be some splutter and splashing...

Success !

:)

Before we get into something that could be hazardous to work with if you have to snake lets talk further about removing the plug and snaking. When you lift the metal plug try to tilt it toward the near wall of the tub. Like rolling it out of the drain holke. There will be a brass articulated rod attached to it. Let us know if it came out.