However,I think the time spent doing this in
primary school should be small and should
progressively build up until the final two years of high school
我想请问 这里两个SHOULD 难道后面一个不可以省略掉吗？ 关于英语里面情态动词 的这方面使用方法的原则是什么呢？ 是都不能够省略还是都可以？

不能省。因为"until the final two years of high school"“高中的最后两年”表将来意味。去掉了后一个should的话，光剩下“progressively build up”体现不出将来时态了，所以第二个should既表主观能动“应该”又同时体现时态。

以下两个例句都对，区别除了两句句型不同（第二句是并列句）外，还有是意义上第二句更突出强调要apologize.

You should get back here right now and apologize to him.
“你应该现在马上回到这来并向他道歉。”

You should get back here right now and you should apologize to him. “你应该现在马上回到这来并且你应该向他道歉。”