1. She washed the dishes in the sink.
2. She washed the dishes at the sink.
3. She washed the dishes in the sink in the kitchen.
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Are they all grammatical? In sentence 3, what does 'in the kitchen' modify?
All are okay.
"in the kitchen" modifies "sink" -- telling where it is. (It's not a bathroom sink.)
Yes, all three sentences are grammatical.
In sentence 3, 'in the kitchen' modifies 'the sink'. It specifies the location of the sink - indicating that the sink is located in the kitchen.
Yes, all three sentences are grammatically correct.
In sentence 3, the phrase "in the kitchen" modifies the noun phrase "the sink." It specifies the location of the sink, indicating that it is in the kitchen.