You know what I think?
I think by the time Rei had broke into the Kudou Mansion he was starting to just...slip.
When he first went undercover, he had done so with Hiromitsu.
After Hiromitsu there was absolutely no one else he could trust to turn to besides Kazami Yuuya, whom he only relies on when it comes to the more mundane tasks, like searching and stuff.
But other than that he was doing it all himself.
And he was starting to slip up, the stress of trying to come up with a cover for everything starting to get to him more and more.
Rum demanding information, for Rei to be quicker in providing information on Mouri Kogoro.
Not to mention, how his own identity was possibly starting to slip up.
And then there is his hatred for Akai that is just so easy to fall back to.
In other words, I sighed in relief when the Kudou parents opened the lights and went 'It's time to sit down and have tea and civil discussions'.
Because, from what I've seen, that was the time when Rei finally managed to find allies.