应该是这样的：这个定语从句the washing machine (that) she had had repaired went wrong gain.
其中that引导词应在从句中had had之后作宾语.我们有个词组have sth done. 本句中的had had就是have的过去完成时（因为went wrong是过去的时态,所以修理的动作就成了过去的过去的,即had had the machine repaired),have sth done中的sth就是省略的引导词that ,done就是本句中的repaired.
went wrong again的主语应是前面的the washing machine.