No, they cannot do both.
Your first situation is the correct one. In the Actions in Combat 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. I would assume that you would carry the standard rules for Trip into this attempt, which would result in you making a ranged touch attack against the target, and then making an opposed STR vs the higher of the opponent's STR or DEX. Though a generous GM might handwave it to a DEX vs opponent, since ranged attacks use DEX instead of STR to hit.