It's most likely that your Parent Layer has a scale value that is not proportionate - something like [80,145], for example.
When you parent a child to such a layer and you rotate the Child Layer, it will inherit the parent's scale. To prevent this skewing/distortion, do the following.
1) Start afresh without any parenting structure in place.
2) Ensure the child layer's scale values are proportionate
3) create a Null Layer and drag it's Anchor Point towards the Anchor Point of the soon-to-be-parent layer - as you drag and get close to the target Anchor Point, hold down the CTRL/COMMAND key to invoke the Snap Feature.
4) Parent the Null Layer to the Parent Layer
5) Parent the original child layer to the Null Layer.
HTH
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