Why did Mycroft and Sherlock disguise themselves to meet Eurus?

Question

In Sherlock S04E03 we see Mycroft disguised as a fisherman along with John Watson to let Sherlock (impersonating a security official) meet Eurus. Time and again in this episode as well as the previous ones, it has been clearly mentioned that Mycroft holds a respectable position in the government; infact he himself is the British Government. Without the direct orders of Mycroft, no one is allowed to diagnose Eurus or even talk to her.

So couldn't Mycroft just order the Sherrinford authorities to let Sherlock meet Eurus.

Why did they undertake so much trouble for the meeting?

Answer 1

This one is explained in the dialogue.

When the Governor has apparently uncovered the disguise, thinking it to be Sherlock, but in fact Mycroft, he protests...

"This is insane, this is unnecessary".

Watson replies...

Watson: "No, your security is compromised and we don't know who to trust."

Governor: "And that justifies dressing up?"

Mycroft: (Vehemently) "Yes, it does!"

So, basically, they don't know who to trust so they start with the person least likely to be involved.

As it turns out, of course, they are wrong.