We do try to keep our controls backwards compatible and the following sticky thread lists all known issues and changes: http://www.telerik.com/forums/known-issues-and-important-changes. You should not need to redesign your pages or rewrite your code after an upgrade.
Generally, an upgrade of our assemblies is a straghtforward procedure that only requires that you update a few assemblies and their project references: http://docs.telerik.com/devtools/aspnet-ajax/installation/upgrading-instructions/upgrading-a-trial-to-a-developer-license-or-to-a-newer-version#upgrade-to-a-newer-version-of-telerik-ui-for-aspnet-ajax.
We do not support the SiteCore environment, however, and I cannot say whether there is something specific they add to the situation (e.g., fully qualified references that may require a bindingRedirect element). I, therefore, advise that you contact their support team for help with this case.
I also feel obliged to note that the 2012 version you have is extremely old and does not support modern browsers like Chrome, Firefox, IE10, IE11 and I strongly advise that you look for ways to upgrade to the latest (2015.1.401 at the time of writing, with Q2 2015 due to be released shortly).
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