I'm sure knowing that he had the support of his mother and the chance to give it up if it got too much for him gave him the strength he needed to go on.

这个句子没错。

结构分析：

I'm sure 后面是省略了that 的宾语从句。I'm sure that knowing...

在宾语从句中：

knowing that he had the support of his mother and the chance to give it up if it got too much for him （主语。动名词结构作主语）gave（谓语动词） him （间接宾语）the strength （直接宾语）he needed to go on.（直接宾语的定语）

【翻译】我确信，认识到他获得了母亲的支持，并且他若承受不了太多就可以有机会放弃，这给了他继续前进所需要的力量。

1. 宾语从句的主要意思是：认识到某事给了他力量。

2. if it got too much for him 是 he had the chance to give it up 的条件从句。——“他若承受不了太多就可以有机会放弃”。