Let somebody do sth,而不是Let somebody to do sth.
who are so young 这个主语从句是用来修饰the children的,如果把这个主语从句去掉,只剩下Let句型,就是Let the children go swimming,这句话是正确的,如果选择A,就成了Let the children to go swimming,这与Let句型不符.然后C,D答案很明显是不正确的!所以选择B!