WolfishMusings’ reply is actually what the Tosafos in Nida answers. Holding the key means that he decides when and where.
You ask, “Everything in the world is controlled by Hashem and angels are shluchim for His will.” That’s a great question. The picture is a bit more complex. Rav Shrira Gaon says that Malachim do have a say in certain matters and it is permissible to request of them some favors.
For a better understanding, recall the Mishna in Avos that Hashem could have created the world in one Maamar but He chose to do it in ten, so as to give S’char to those who hold up this large complex world. It might sound almost trivial to us, one word, ten words. But we understand that each Maamar was introducing a new system by which the world would be run.
If everything would be run directly from the highest order, there would not be any confusing events. Reward and punishment would be instant, Parnasa would be directly linked to the person’s Zechusim, and everything would be very clear. Now, there is a system on top of system. This causes the desired amount of ambiguity, that allows for what we know of as Teva.
This is all Ratzon Hashem, and everything catches up, but things take time and are rarely clear. Mikra Echad Latzadik Vilarasha, Kivan Shenitan Reshus… It’s like creating a detailed painting with a wide brush. If you plan it out well enough it can be done, but each stroke effects more than the desired area.