I’ll ask again, since you ducked the question: If Congress set a restrictive ROE, would that supersede the orders of the CINC, in your opinion?
In short, who runs the battlefield, the CINC, or Congress?
Your question is flawed in its premise.
“Who runs the battlefield” is too generalized. The President is the Commander in Chief and Congress has war powers as well.
The President, through the Executive Branch decides the overall strategy of the war...however, Congress may restrict Executive powers (See War Powers Act).
The Congress is authorized to generally run the military and regulate the military, however. This comes into play in this situation. The President has dictated ROE to the Generals, who follow the Presidents’ orders.
However, the Congress has every right as stipulated in the Constitution to write law to right something, they as Congress, see as fatally flawed. The current ROE is fatally flawed.
Divided government has peculiar strife which was forseen by the Founders. The Supreme Court has for the most part ruled that they will not decide these issues and will let them play out in the political arena. In other words, the Executive and Legislative will have to fight it out.