Imagine the following star system: The star is very much like ours. Orbiting this star is one planet, very much like Earth. Let's call it the Orb. Orbiting the Orb are two moons: a large one, Mona, that is very much like ours and a small one, Wick, that's big enough to be round but small enough to not cause havoc on the Orb with it's rather close orbit. There is nothing else in the system, not even a mote of dust, and the system itself is in a very quiet neighborhood.
An Orb day, specifically a sidereal day, is very close to twenty-four Earth hours long but unlike an Earth day is always exactly the same length, every day. An Orb year, specifically a tropical year, is exactly 364 Orb days long. An Orb month, the length of Mona's phase cycle, is exactly one-twelfth of an Orb year (i.e., there are exactly twelve months in a year.) An Orb week, the length of Wick's phase cycle, is exactly 7 Orb days long, meaning there are exactly 52 weeks in a year.
Now obviously this system can't maintain this level of precision indefinitely. And in fact the system isn't natural, but was created and maintained by outside entities. For story reasons, these entities are to be permanently removed and nature is to take its course. My question is how quickly and how catastrophically would the system as described destabilize. My first guess is that Wick, in a 3:13 resonance with Mona, would start moving pretty fast, but I don't know which way or how soon.
Also: Assume Wick is sturdy enough that its Roche limit is within its orbit. If this simply isn't possible, although I doubt it isn't, please say so.