so much homework did we have to do that we don't have a rest.

这是部分倒装的一种形式，当so + adj/adv. 放在句首时，就倒装。
如：So excited was the boy that he couldn't sleep kast night.
So fast did he run that he wa soon ahead of others.

强调 加强语气 表现作也确实十分得多

so much homework did we have to do that we don't have a rest.

原句可改写为：“we have to do so much homework so that we don't have a rest.”

"so much homework "在这里是被强调的，由于提前了这个词组，就不得不倒装，以保持全局的平衡。