> The various executive branch departments were created by Congress

Yes

> and are supposed to follow the instructions given by Congress.

Well, yes, but also no. Executive agencies must adhere to the law, but Congress cannot fully set the Executive's policy. Congress has very limited powers to force policy on the Executive, mainly advice and consent (for appointments and treaty ratification) and impeachment.

Past Presidents have wielded vastly more power relative to Congress than the current one. You should see the things that Lincoln did! Lincoln: suspended Habeas Corpus even though the Constitution says only Congress can, he abrogated treaties against the will of the Senate even though the Senate believed that since ratification requires their advice and consent then so much abrogation (but the Constitution is silent on the matter of abrogation) and as a result modern treaties have abrogation clauses to try to hem in heads of state but obviously those clauses can only go so far, and many other things. President Jefferson denied Adams' 18 lame duck federal judge appointees their commissions (and Marbury had something to say about that, namely that it was unconstitutional but also that he couldn't do anything about it). And that's just some of the notable things that Presidents have done that Congress (or in Jefferson's case, the preceding Congress) didn't like.