Following code gets the property of the particular web part, so now you need to place it in appropriate event for 'consumer' web part and assign the value of the property you need.
CMSAbstractWebPart webpart1 = PagePlaceholder.FindWebPart("WebPart1");
string wp1Container = ValidationHelper.GetString(webpart1.GetValue("Container"), "");
To avoid web part customization, I'd recommend creation of the alternative layout for the 'consumer' web part, which will be the same as default +
<script runat="server"> your handler for onLoad, or any better event </script>