Объединить массив в один

            Array
    (
 [0] => Array(
    [order_id] => 52
    [firstname] => test
    [lastname] => tst
    [email] => Test
    [telephone] => test
    [payment_address_1] => Отделение №1: ул. Гагарина,22
    [payment_method] => Новая почта
    [date_added] => 2017-03-15 15:51:44
    [date_modified] => 2017-03-15 15:51:44
    )
)

    Array
    (
        [0] => Array
        (
        [order_product_id] => 281
        [id_order] => 52
        [name] => Тапочки
        [model] => Закрытые
        [quantity] => 1
        [total] => 25.00
        [oll_total] => 25.00
    )
[1] => Array
    (
        [order_product_id] => 280
        [id_order] => 52
        [name] => Носки
        [model] => Закрытые
        [quantity] => 1
        [total] => 20.50
        [oll_total] => 20.50
    )

        Array
    (
        [0] => Array(
            [order_id] => 52
    [firstname] => test
    [lastname] => tst
    [email] => Test
    [telephone] => test
    [payment_address_1] => Отделение №1: ул. Гагарина,22
    [payment_method] => Новая почта
    [name] => Тапочки,Носки
    [oll_total] => 25.00+20,05
    [date_added] => 2017-03-15 15:51:44
    [date_modified] => 2017-03-15 15:51:44
)

Просто сложите массивы:

         $arr1 = array(
                    [
                    "order_id" => 52,
                    "firstname" => "test",
                    "lastname" => "tst",
                    "email" => "Test",
                    "telephone" => "test",
                    "payment_address_1" => "Отделение №1: ул. Гагарина,22",
                    "payment_method" => "Новая почта",
                    "date_added" => "2017-03-15 15:51:44",
                    "date_modified" => "2017-03-15 15:51:44 "
            ]
     ) ;
    $arr2 = array(
            [
                    "order_product_id" => 52,
                    "id_order" => 52,
                    "name" => "Носки",
                    "model" => "Закрытые",
                    "quantity" => 1,
                    "total" => 25.00,
                    "oll_total" => 25.00,
            ],
            [
                    "order_product_id" => 280,
                    "id_order" => 52,
                    "name" => "Тапочки",
                    "model" => "Закрытые",
                    "quantity" => 1,
                    "total" => 25.00,
                    "oll_total" => 25.00,
            ],
    ) ;

    $result = $arr1 + $arr2;

Результат:

http://prntscr.com/ekltaa

всё более чем очевидно

$order['products'] = $order_product

Для объединения массивов можно использовать merge()
Что-то типо такого:

var arr1=[1,2,3];<br>
var arr2=["a","b","c"];<br>
$.merge(arr1, arr2);

Вариант 1. Запрос в базу. Пример для MySQL:

SELECT o.*, GROUP_CONCAT(op.name SEPARATOR ', ') AS name, SUM(op.oll_total) AS oll_total 
FROM order_table o
LEFT JOIN order_product_table op ON op.order_product_id = o.order_id
GROUP BY o.order_id

Вариант 2. Цикл в PHP, если у вас 2 массива

$result = [];
foreach ($orders as $key => $order)
{
    $result[$key] = $order + ['name' => [], 'oll_total' => 0];
    foreach ($order_products as $key2 => $product)
    {
        if ($product['order_product_id'] == $order['order_id'])
        {
            $result[$key]['name'][] = $product['name'];
            $result[$key]['oll_total'] += $product['oll_total'];
        }
    }
    $result[$key]['name'] = implode(', ', $result[$key]['name']);
}

Готовой функции нет. В вашем конкретном случае я бы выбрала вариант 1.