I know her children _____ (be) reliable.

填 to be，不填 being，也不填be。再举例如下：

We know her to be honest. 我们知道她很诚实。

They knew him to be a spy. 他们知道他是一个间谍。

They knew him to be a dangerous criminal. 他们知道他是个危险的罪犯。

如果不是动词 be，也可以省略 to。如：

I never knew him (to) act without thinking. 我从未发现他轻率行事过。

不过，如果 know 用于被动语态，或后面的不定式为完成式，通常不宜省略 to。如：

He was known to abuse alcohol. 他酗酒是众所周知的事。

He is known to have committed crimes. 众所周知他犯下了种种罪行。