class MyPopup(QWidget):
    def __init__(self):
        QWidget.__init__(self)
        textField = QLineEdit(self)
        textField.setGeometry(50, 50, 300, 20)
        btn1_del = QPushButton(u"создать вкладку", self)
        btn1_del.clicked.connect(lambda: MainWidget().add_new_tab(textField.displayText()))
        btn1_del.move(150, 100)

class MainWidget(QWidget):
...
        self.tab_widget = QTabWidget()
        self.tab_widget.setCornerWidget(self.tabButton)
        self.tabButton.clicked.connect(self.open_popup_tab)
        self.tab1 = QWidget()
        self.tab_widget.addTab(self.tab1, u"Узлы")
...
    def add_new_tab(self, tab_tittle):
        print(tab_tittle)
        new_tab = QWidget()
        self.tab_widget.addTab(new_tab, u"11")