In or during tough times would be more common. These suggest time periods, whereas at suggests a physical place. At a difficult crossroads in his life, he was in a dilemma. In this case, in suggests entanglement or involvement with the dilemma, so while in tough times would be acceptable by the same reasoning, it's simply not used that way as often in speech.
Pa's is possessive. Change it to the possessive pronoun "his" for example. Not Irish ones like his. Now substitute the name of the person instead of the pronoun: Not Irish ones like Bill's (or Pa's).
And of course, in the example above the "...parents were" is implied, so it's not spoken. The speaker means to say, "not Irish ones like my pa's parents were."
An interesting sidebar. If there are two or more people listed, only the last one gets the possessive treatment: Not Irish ones like Bill and Mary and John's. UNLESS of course, you want to stress individual ownership. If Bill and Mary and John each have their own different Irish parents, then you list it this way: Not Irish ones like Bill's and Mary's and John's parents were. But if they were siblings (brothers and sisters of the same parents) it would be "Not Irish ones like Bill and Mary and John's parents were."
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