beginners question - create an element

Hello, just starting to learn how to work with XML via Java and I have encountered an error.

I have an XML file with car owners and their cars.
XML file:

Code:

---

<?xml version="1.0" encoding="utf-8"?>
<people>
    <person id="1">                  <!-- id is required, unique (positive) integer
                                      (no two cars with same ID) -->
        <name>Pavel</name>        <!-- name is required, non-empty string -->
        <surname>Novák</surname> <!-- surname is required, non-empty string -->
        <salary>12000.00</salary>  <!-- salary is required, positive number
                                          with 2 decimal places precision, e.g. 10000.50 -->
        <note>Poznámka</note>    <!-- note optional element, repeatable, contains any string -->
        <cars>                        <!-- cars optional element, contains any number of child-element car -->
            <car id="ZNC 33-93"> <!-- id is required, format like this: LLL NN-NN where L is a letter, N a ciphers 0..9
                                      two or three letters, space, two ciphers, comma and 2 ciphers) -->
                <type>Škoda 120 GLX</type> <!-- type is required, non-empty string -->
                <fuel>gasoline</fuel>      <!-- fuel is required, enumeration with values:
                                                gasoline/diesel/lpg/electricity -->
                <year>1985</year>          <!-- year is required, 4-ciphers positive integer number -->
                <country>cz</country>          <!-- country is required, 2 chars string -->
                <price>15000</price>        <!-- price is required, positive integer -->
            </car>
        </cars>
    </person>

    <person id="2" age="21">
        <name>Libor</name>
        <surname>Polák</surname>
        <salary>9000.00</salary>
    </person>

    <person id="3">
        <name>Jan</name>
        <surname>Hroza</surname>
        <salary>68475.25</salary>

        <cars>
            <car id="6B6 82-51">
                <type>Škoda Octavia Combi</type>
                <fuel>UNKNOWN</fuel>
                <year>2009</year>
                <country>cz</country>
                <price>200000</price>
            </car>
            <car id="ZNH 28-51">
                <type>Škoda Octavia Combi</type>
                <fuel>diesel</fuel>
                <year>2001</year>
                <country>cz</country>
                <price>50000</price>
            </car>
            <car id="ZNE 11-75">
                <type>Škoda Favorit</type>
                <fuel>lpg</fuel>
                <year>1995</year>
                <country>cz</country>
                <price>20000</price>
            </car>
            <car id="ZN 85-51">
                <type>Prototyp č. 1 vyrobený v dílně Franty Vomáčky</type>
                <fuel>electricity</fuel>
                <year>1995</year>
                <country>cz</country>
                <price>150000</price>
            </car>
        </cars>

    </person>

</people>

---

And I want to write a method, that changes the owner of the car, i.e. moves the car element to another person.
Here is what I got so fat, it seems to remove the element, but does not create the new one>

Code:

---

public class Main {

    /**
    * W3C object model representation of a XML document.
    * Note: We use the interface(!) not its implementation
    */
    private Document doc;

    /**
    * Task 1, part A: Complete this method.
    *
    * Sells the car identified by carId to the person identified by personId.
    * (i.e. moves the respective car element into the cars element
    * of the recipient person, new owner.
    * Note that if the recipient does not have any cars yet,
    * the containing cars element must first be created before
    * the cars is moved into it.
    * if either the car or the recipient is not present, the method
    * does not change nor report anything.
    *
    * @param carId id of the car to be sold
    * @param personId person receiving the car
    * @throws IllegalArgumentException if any parameter is null or empty
    */
    public void sellCarTo(String carId, String personId) {
        Element car = null;
        Element person;
        Element pomCar = null;
                       
        NodeList carList = doc.getElementsByTagName("car");
       
        for(int i = 0; i < carList.getLength(); i++) {
            car = (Element) carList.item(i);           
            String pomCarId = car.getAttribute("id");
                             
            if(pomCarId.equals(carId)) {
                String myCarId = pomCarId;
                pomCar = car;
                car.getParentNode().removeChild(car);               
            }
        }
         
        NodeList peopleList = doc.getElementsByTagName("person");       
       
        for(int i = 0; i < peopleList.getLength(); i++) {
            person = (Element) peopleList.item(i);
            String pomPersonId = person.getAttribute("id");
                                   
            if(pomPersonId.equals(personId)) {
                Element newCar = null;
                NodeList cars = person.getElementsByTagName("cars");
               
                if(cars.getLength() == 0) {
                    newCar = doc.createElement("cars");
                    person.appendChild(pomCar);
                } else {
                    newCar = (Element) cars.item(carList.getLength() + 1);
                }
                newCar.appendChild(pomCar);
            }
        }
    }

---

And I can´t really find the problem. If anyone can point me in the right direction, I would be really grateful.