We see our kids college background as a prize demonstrating how well weve raised them.
结构分析
主干：We see...background as a prize...
谓语部分用了see...as...的句型，表示把......看做......，as 引导的介词短语作宾语补足语。现在分词短语demonstrating作后置定语修饰a prize, how 引导的从句作demonstrating的宾语。
译文：我们把子女的大学教育背景当成是证明我们如何成功养育子女的奖品。