My question is would the trigger doubling from Yarok, The Desecrated work with a land like Thriving Grove making it a tri land, or would it just choose another color and only work like it originally would?
Thriving Grove doesn't have any triggered ablities, so Yarok has nothing to make trigger twice. What the Grove has is a static ability that creates a replacement effect. A triggered ability always uses the words "when", "whenever" or "at". If neither of those words is present, you are not dealing with a triggered ability.
113.3c Triggered abilities have a trigger condition and an effect. They are written as “[Trigger condition], [effect],” and include (and usually begin with) the word “when,” “whenever,” or “at.” Whenever the trigger event occurs, the ability is put on the stack the next time a player would receive priority and stays there until it’s countered, it resolves, or it otherwise leaves the stack. See rule 603, “Handling Triggered Abilities.”
614.1c Effects that read “[This permanent] enters the battlefield with . . . ,” “As [this permanent] enters the battlefield . . . ,” or “[This permanent] enters the battlefield as . . . ” are replacement effects.
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