Take a look at the sentence again:
Rachel painstakingly ironed her linen shirt all
the while, she was thinking how pointless this chore was since linen begins
to wrinkle the moment after the last button is fastened.
For a sentence to be a comma splice, you must have two complete sentences joined with a comma. In the example above, there is no comma. Rachel painstakingly ironed her linen shirt is one sentence. All the while, she was thinking … begins the second sentence. Because only empty space exists between the two, you should call this error a fused sentence.
Remember that both comma splices and fused sentences are major errors. They make your reader think that you cannot write a correct sentence. Because the sentence is the most basic building block of a piece of writing, comma splices and fused sentences make you look like an amateur!
To fix the problem above, you could put a period after shirt and begin all with a capital A.