Please always simplify samples before posting.
Your initial sample might be simplified to the one below, but still reproduces the problem.
Example
<%@ Page Language="C#" %>
<%@ Register Assembly="Ext.Net" Namespace="Ext.Net" TagPrefix="ext" %>
<script runat="server">
[DirectMethod]
public void Expand()
{
this.Panel1.Expand();
}
</script>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head runat="server">
<title>Ext.NET Example</title>
</head>
<body>
<form runat="server">
<ext:ResourceManager runat="server" />
<ext:Viewport runat="server" Layout="FitLayout">
<Items>
<ext:Panel runat="server" Region="Center" Layout="AccordionLayout">
<Items>
<ext:Panel runat="server">
<Items>
<ext:Button runat="server" Text="Click me to expand the next panel">
<Listeners>
<Click Handler="Ext.net.DirectMethods.Expand();" />
</Listeners>
</ext:Button>
</Items>
</ext:Panel>
<ext:Panel
ID="Panel1"
runat="server"
HideMode="Offsets"
Layout="ColumnLayout">
<LayoutConfig>
<ext:ColumnLayoutConfig Split="true" />
</LayoutConfig>
<Items>
<ext:Container runat="server" ColumnWidth="0.5" Layout="BorderLayout">
<Items>
<ext:Panel runat="server" Region="Center" Html="Left" />
</Items>
</ext:Container>
<ext:Container runat="server" ColumnWidth="0.5" Layout="BorderLayout">
<Items>
<ext:Panel runat="server" Region="Center" Html="Right" />
</Items>
</ext:Container>
</Items>
</ext:Panel>
</Items>
</ext:Panel>
</Items>
</ext:Viewport>
</form>
</body>
</html>
Removing HideMode="Offsets" of the Panel1 fixes the problem.