首先我们应当知道一个短语
keep near to sb.靠近,接近……
然后我们应该知道 as adj.as one can= as adj.as possible
那么 其实这个句子应该这样读
The woman kept as near as she could/ to the children and even tried to get into the case herself.
这种插入形的句子在英语中非常常见,通过状语和定语来分割开来
例如：
I will try everything I can to help you.
所以,在英语学习中要把眼睛拉长一些,这样就后事半功倍了!