おばあさん は 川（かわ） へ せんたく に でかけます。
Why is there both へ and に? When can they be used together? Can someone break down the sentence for me to understand?
The に you presented indicates purpose of going rather than a direction.
Sentence: The woman goes out to the river to do laundry.
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As far as I know it's fine to use に after both verb stems and nouns when given as reasons for something.
E.g. お土産に買う - I will buy it as a souvenir
And to give a more concrete answer to your question: The particles convey different information, one is direction and the other is reason. Of course you can't have two directions, but that is not the case here.