Child skews when parenting

This is caused by non-uniform scaling on rotated children (so you can read about it.) You can't fix it directly, but you can rearrange things to avoid it.

http://answers.unity3d.com/questions/21702/making-object-a-child-causes-distortionskewing.html has more discussion/answers. I'm sure there are others.

I found some similar threads, such as the one you linked to, but all of them refer to parenting DURING the game. I'm parenting the object BEFORE running the game.

Given that this is caused by the children being rotated before parenting, I tried setting the rotation to 0, parenting, then rotating again. Same problem.

Doesn't matter. The problem is that it's applying it's parent's scale after it does the rotation, and having trouble reconciling the two. In general, it's just a really bad idea to have an object be a child of a non-uniform scaled object.

I would make an empty GameObject that is the parent of both. That way they can have individual scales, but will still follow the same transform.

I tried this, but the hammer has its own collision box- meaning that pushing up against a wall separates the two. It also messes up my jumping script.