Parent kategorilere optgroup tanimladiginizda sorun hallolur gibi.
Mobildeyim kodlarini duzenleyemedim. Asagidaki kodu kendine gore duzenleyebilirsin.

<select name="" id="">
@forelse ($categories as $category)
<optgroup label="{{$category->name}}">
@forelse($category->child as $child)
<option value="{{$child->id}}">{{$child->name}}</option>
@empty
<option value="">No category</option>
@endforelse
</optgroup>
@empty @endforelse
</select>