It sounds like there's some stuff in your analogy that is similar to the QM situation. I would caution against placing too much emphases on these analogies thou

It sounds like there's some stuff in your analogy that is similar to the QM situation. I would caution against placing too much emphases on these analogies though since a very important aspect of all of this is not just that the two systems are correlated but rather that they are entangled. There's a classic analogy to this when we talk about entanglement: imagine taking a pair of gloves and mixing them up. Put one in one box and the other in another box. Send one of the boxes far away. When you look down at the box that you kept, there is no way of knowing if it contains a left handed or a right handed glove; it's a 50/50 shot either way. Similarly you have no idea what the other box contains. You then decide to open your box and find a right handed glove. You then immediately know that the other box contains a left handed glove. In some sense this feels similar to what we see in entanglement but I don't think most people would claim that you opening your box somehow compelled the other glove to pick left/right. They were just always that way, you just didn't know which glove was where. The claim, however, is that in QM it's not like this. Instead, your act of measuring your system actually does compell the other system to change. For a long time there were a lot of heated arguments around all of this (most prominently between Einstein and Bohr) trying to figure out if the state of either box was truly undecided until you opened it or if there could have been some type of "hidden variable" that we had yet not discovered that nonetheless dictated what the state was (i.e. could it be more like the glove example or was it truly a new "spooky action at a distance"?) For a long time physicists believed that this was an unanswerable question and should be relegated to philosophy. It wasn't until Bell discovered his inequality that this was dispelled. He designed an experiment that could be conducted to tell the two stories apart. When it was carried out, it was determined that nature is not like the glove example but rather consistent with the truly quantum story around entanglement. In other words, your measurement of your system actually does compelled the other system to change.