Pressing Space key when typing in TextBox in Expander's Header expands the control.

The root cause is not located in the RadExpander control. If using Microsoft ToggleButton with TextBox inside the space key will trigger a button click. This issue is for Silverlight platform.
The same sample in WPF does not trigger a button click.

This issue is reproducible when you host the RadExpander in a ControlTemlate targeting the native ListBoxItem.

DECLINED: XAML Team reviewed this item and taking into account the current state of SIlverlight platform decided not to address it in the future.