
I have a couple of ideas to why Amou would keep it from Misumi.
I don't think Misumi would ever hurt Doumeki but when it comes to Yashiro, Misumi is honest to a fault and he'd eventually slip. Amou is more aware of his surroundings and I think he wants to respect Yashiro's wish of keeping Doumeki away. Another reason might be because Misumi could pressure Yashiro of joining him using Doumeki and I think Amou wants to avoid that too.
Now about Nanahara, he wanted to help Doumeki but he's still Yashiro's underling and I think he resorted to Amou because he has more connections than him and would be able to hid Doumeki well. Also, Nanahara can't keep things from Yashiro that's why I think he asked Amou like (hide him so well, even I can't find him) and if he doesn't know, he can't tell.

I love Misumi but I always had this nagging feeling he is possessive towards Yashiro to the point that he would rather have a miserable Yashiro still in his world in the Yakuza that let him be happy and free somewhere ... thus my feeling that he could even get rid of Doumeki if he feels that he is Yashiro escape. However, the overall consensus is that Misumi loves Yashiro in his own way so I suppose what you guessed makes more sense... Thank you! :)
Now I'm wondering why Amou is hiding the favor from Misumi. Did I miss anything?
Is it because Misumi would do harm to Doumeki?
I remember Nanahara wanted to help Doumeki but how would he have leverage with Amou to ask him that? They don't seem close.