The InlineUIContainers have a property UiElement, which holds a reference to the UIElement that is embedded within it. That would give you a reference to your custom button. Starting from there, you should be able to access all elements along the way down to the text box.
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the Telerik team
Registration for Q1 2011 What’s New Webinar Week is now open. Mark your calendar for the week starting March 21st and book your seat
for a walk through all the exciting stuff we ship with the new release!