QML/C++ model - view separation: data in C++, mult

Question

I am trying to strictly separate the data (in C++) from the visualization (lists in QML). On the model side, data is stored in instances of a C++ class (Data.cpp) and pointers to that instances are arranged in two lists (completeList and selectedList) by another C++ class (Parser.cpp). Those two lists should be displayed in QML, with the following restrictions:

• the data in completeList is displayed in different QML ListViews (for example according to the name)
• this separation must be done in QML, not by Parses.cpp (which only provides the complete list)
• it must be possible to add list items from completeList to selectedList (for example by clicking on it)
• if values of Data are changed in one ListView, the Data itself and the other views displaying this Data should change accordingly

Thanks to ksimons, I found a way to do half of it, but I cant figure out the rest. Here is what I got so far:

Data.h

class Data : public QObject
{
    Q_OBJECT
    Q_PROPERTY(QString name READ name WRITE setName NOTIFY nameChanged)

public:
    Data(const QString &n) : _name(n) { }
    QString name() const { return _name; }

    void setName(const QString &n) {
        if (_name == n)
            return;
        _name = n;
        emit nameChanged(n);
    }

signals:
    void nameChanged(const QString &n);

private:
    QString _name;
};

Parser.h

class Parser : public QObject
{
    Q_OBJECT
    Q_PROPERTY(QQmlListProperty<Data> completeList READ completeList CONSTANT)
    Q_PROPERTY(QQmlListProperty<Data> selectedList READ selectedList CONSTANT)

public:
    Parser(QObject *parent = 0) {
         Data* d1 = new Data(QStringLiteral("a1"));
         Data* d2 = new Data(QStringLiteral("a2"));
         Data* d3 = new Data(QStringLiteral("a3"));
         Data* d4 = new Data(QStringLiteral("b1"));
         Data* d5 = new Data(QStringLiteral("b2"));

        _completeList.append(d1);
        _completeList.append(d2);
        _completeList.append(d3);
        _completeList.append(d4);
        _completeList.append(d5);

        _selectedList.append(d1);
        _selectedList.append(d4);
    }

    QQmlListProperty<Data> completeList() {
        return QQmlListProperty<Data>(this, _completeList);
    }
    QQmlListProperty<Data> selectedList() {
        return QQmlListProperty<Data>(this, _selectedList);
    }

private:
    QList<Data*> _completedList;
    QList<Data*> _selectedList;
};

QML part:

ListView
{
    id: startsWithA
    anchors.fill: parent
    delegate: delegateItem
}
ListView
{
    id: startsWithB
    anchors.fill: parent
    delegate: delegateItem
}
ListView
{
    id: selectedData
    anchors.fill: parent
    delegate: delegateItem
}
Item 
{
     id: delegateItem
     height: 30
     width: parent.width

     Text { text: name }

     MouseArea { //change name of corresponding Data and other views accordingly
     anchors.fill: parent
     onClicked: model.name = "newName";} //does not work

     MouseArea { //add to selectedList in Parser
     anchors.fill: parent
     onClicked: ?????? }
}
Component.onCompleted:
{
    selectedData.model = parser.seletedList;
    var listAll = parser.completeList;
    var listA, listB;
    for(var i=0; i<listAll.length; i++)
    {
        if(listAll[i].name.charAt(0) == 'a')
        {
            //changing values in startsWithA does not affect anything else with that :(
            listA.append(listAll[i]); 
        }
        else if(listAll[i].name.charAt(0) == 'b')
        {
            //changing values in startsWithB does not affect anything else with that :(
            listB.append(listAll[i]); 
        }
        //...
    }
    startsWithA.model = listA;
    startsWithB.model = listB;
    //...
}

I hope this question is not to specific and somebody can help me. Thank you in advance.