at school.

First, you do realize that legislature is a part of the government federal or state, right? Secondly, it is true that president cannot appoint or dismiss, during normal circumstances, governor of a state. Pay attention to the word normal. However, avoid Federal Preemption of State Laws and Policies by the federal government is a mere guideline, not a legal confine.  At the same time, governors of states also recognize the need for federal intervention should states fail to act collectively on issues of legitimate concern. Preemption of state laws, however, should be the exception rather than the rule. But, nothing prohibits federal government from interference of or even superseding the authority of state government. Case in point, during civil war, Lincoln had dismissed governors from “states rebellious against the federal government”. Last but not the least, state has no authority to act likewise to the federal government.