Not close float window when change tab item

Question

Currently, I develop a WPF application containing a TabControl to allow the access to each plugin.

Each plugin uses AvalonDock and has different windows which can be docked, floated or hidden.

When I float a window in the plugin1 and after I switch plugin in the plugin2, the floated window disappears (that is normal) but I would like the floated window of the plugin1 does not disappear when I switch in the plugin2 (like the following screen).

step 1:

step 2:

step 3:

Current code with the disappearance of the floated window

        <TabControl>
        <TabItem>
            <TabItem.Header>
                <StackPanel Orientation="Horizontal">
                    <TextBlock Text="Blue" Foreground="Blue" />
                </StackPanel>
            </TabItem.Header>
            <xcad:DockingManager x:Name="DockingManager">
                <xcad:LayoutRoot>
                    <xcad:LayoutPanel Orientation="Horizontal">
                        <xcad:LayoutDocumentPaneGroup Orientation="Vertical" x:Name="ScriptGroup">
                            <xcad:LayoutDocumentPane x:Name="ScriptPanel" PaneName="ScriptPanel">
                                <xcad:LayoutDocument Title="1-1" >
                                    <TextBlock Text="1-1" Foreground="Blue"  />
                                </xcad:LayoutDocument>
                                <xcad:LayoutDocument Title="1-2">
                                    <TextBlock Text="1-2" Foreground="Blue" />
                                </xcad:LayoutDocument>
                                <xcad:LayoutDocument Title="1-3">
                                    <TextBlock Text="1-2" Foreground="Blue" />
                                </xcad:LayoutDocument>
                                <xcad:LayoutDocument Title="1-4">
                                    <TextBlock Text="1-2" Foreground="Blue" />
                                </xcad:LayoutDocument>
                            </xcad:LayoutDocumentPane>
                        </xcad:LayoutDocumentPaneGroup>
                    </xcad:LayoutPanel>
                </xcad:LayoutRoot>
            </xcad:DockingManager>
        </TabItem>
        <TabItem>
            <TabItem.Header>
                <StackPanel Orientation="Horizontal">
                    <TextBlock Text="Red" Foreground="Red" />
                </StackPanel>
            </TabItem.Header>
            <xcad:DockingManager x:Name="DockingManager2">
                <xcad:LayoutRoot>
                    <xcad:LayoutPanel Orientation="Horizontal">
                        <xcad:LayoutDocumentPaneGroup Orientation="Vertical" x:Name="ScriptGroup2qdrgqr">
                            <xcad:LayoutDocumentPane x:Name="ScriptPanel2qrgtqr" PaneName="ScriptPanel">
                                <xcad:LayoutDocument Title="1-1">
                                    <TextBlock Text="1-1"  Foreground="Red" />
                                </xcad:LayoutDocument>
                                <xcad:LayoutDocument Title="1-2">
                                    <TextBlock Text="1-2" Foreground="Red"/>
                                </xcad:LayoutDocument>
                                <xcad:LayoutDocument Title="1-3">
                                    <TextBlock Text="1-2" Foreground="Red"/>
                                </xcad:LayoutDocument>
                                <xcad:LayoutDocument Title="1-4">
                                    <TextBlock Text="1-2" Foreground="Red"/>
                                </xcad:LayoutDocument>
                            </xcad:LayoutDocumentPane>
                        </xcad:LayoutDocumentPaneGroup>
                    </xcad:LayoutPanel>
                </xcad:LayoutRoot>
            </xcad:DockingManager>
        </TabItem>
        <TabItem>
            <TabItem.Header>
                <StackPanel Orientation="Horizontal">
                    <TextBlock Text="Green" Foreground="Green" />
                </StackPanel>
            </TabItem.Header>
            <xcad:DockingManager x:Name="DockingManager3">
                <xcad:LayoutRoot>
                    <xcad:LayoutPanel Orientation="Horizontal">

                        <xcad:LayoutDocumentPaneGroup Orientation="Vertical" x:Name="ScriptGroup3">
                            <xcad:LayoutDocumentPane x:Name="ScriptPanel3" PaneName="ScriptPanel">
                                <xcad:LayoutDocument Title="1-1">
                                    <TextBlock Text="1-1" Foreground="Green" />
                                </xcad:LayoutDocument>
                                <xcad:LayoutDocument Title="1-2">
                                    <TextBlock Text="1-2" Foreground="Green"/>
                                </xcad:LayoutDocument>
                                <xcad:LayoutDocument Title="1-3">
                                    <TextBlock Text="1-2" Foreground="Green"/>
                                </xcad:LayoutDocument>
                                <xcad:LayoutDocument Title="1-4">
                                    <TextBlock Text="1-2" Foreground="Green"/>
                                </xcad:LayoutDocument>
                            </xcad:LayoutDocumentPane>
                        </xcad:LayoutDocumentPaneGroup>
                    </xcad:LayoutPanel>
                </xcad:LayoutRoot>
            </xcad:DockingManager>
        </TabItem>
    </TabControl>

Is it possible to do this by kept the current mechanism ? (with Tabcontrol & Avalondock)

If the answer is no, can you say me what is the best way to do this please ?