Well, that is something. So, at the moment when you need to create the smaller model, you have selected items from big models. Now, you can add a method to your C++ model (make it Q_INVOKABLE so it's available from QML) which takes item indexes (or, if your items have some unique IDs, you can use them here, too). Use that method on QML side (I imagine you have some button that user will click when items are selected - that's where this method should be used).
Now, in the C++ method, create a new small model and send it to QML via signal. Or, if you already have the small model, just send the data to it and make sure proper signals are emitted (beginInserRows(), beginResetModel(), dataChanged() etc. depending on how you do the update).