set validation group on validation control and button and use update panel for asynchronously bind drop down on selected Chang Event of another drop down
use update panel like
first declare ScriptManager your page
<asp:ScriptManager ID="ScriptManager1" runat="server">
</asp:ScriptManager>
<asp:dropdownlist id="ddl1" runat="server" enableviewstate="False" >
</asp:dropdownlist>
<asp:UpdatePanel ID="UpdatePanel1" runat="server">
<ContentTemplate>
<asp:dropdownlist id="ddl2" runat="server" enableviewstate="False">
</asp:dropdownlist>
</ContentTemplate>
<Triggers>
<asp:AsyncPostBackTrigger ControlID="ddl1" EventName="SelectedIndexChanged" />
</Triggers>
</asp:UpdatePanel>