What do your relationships look like? If you have a car relationship on the vehicle model, and it's a one-to-one relationship (each vehicle is tied to only one car) you could just do
public function update(Request $request, $id)
{
$vehicle = Vehicle::find($id);
$vehicle->name = $request->input('name');
$vehicle->owner = $request->input('owner');
$vehicle->save();
//update the fuel for this car belonging to the vehicle
$vehicle->car()->update(['fuel' => $request->input('fuel')]);
}
https://laravel.com/docs/5.7/eloquent-relationships#inserting-and-updating-related-models