**No**, they cannot do both.  

Your first situation is the correct one. In the <a href="http://www.systemreferencedocuments.org/resources/systems/pennpaper/dnd35/soveliorsage/actionsInCombat.html">Actions in Combat</a> section of the SRD, Disarm, Grapple, and Trip are given a footnote that reads (emphasis mine): 
>These attack forms *substitute for a melee attack*, not an action. As melee attacks, they can be used once in an attack or charge action, one or more times in a full attack action, or even as an attack of opportunity.

A "Trip Attack" is an attack that substitutes damage for applying the prone condition to the opponent after a contested roll.