How do I query a deep relationship in laravel and filter parents by children?

What you're looking for is whereHas(). Also you can write with(array('products.skus')) directly without products

$category = new Category();
$categories = $category->with(array('products', 'products.skus' => function ($query) {
        $query->where('price', '>', 10);
    }))
    ->whereHas('products.skus', function($query){
        $query->where('price', '>', 10);
    })->get();

You need both, with and whereHas but you can simplify the code a bit by putting the closure in a variable:

$priceGreaterTen = function($query){
    $query->where('price', '>', 10);
};

$category = new Category();
$categories = $category->with(array('products', 'products.skus' => $priceGreaterTen))
                       ->whereHas('products.skus', $priceGreaterTen)
                       ->get();