@jnette3,
I think the preposition "in" is fine. I think the noun "times" is incorrect. You could write "In this way, you can find the lighter dog in two
trials."
I actually prefer the first sentence.
"In this way, you can find the lighter dog while using the scale only twice."
or you could say
"In this way, you can find the lighter dog while using the scale only two times."
Actually I think I like this last one the best.