class Invoice extends Model
{
    public function invoiceProduction()
    {
        return $this->hasOne(InvoiceProduction::class, 'invoice_id', 'id');
    }
}

class InvoiceProduction extends Model
{
    public function production()
    {
        return $this->hasOne(Production::class, 'production_id', 'id');
    }
}

class Production extends Model
{

}

$invoice = Invoice::with(['invoiceProduction' => function ($query) {
    $query->with('production');
}])->get();

$invoice[0]->invoiceProduction->production;

应该是这样，我没验证。