Non-scientist question about special relativity and quantum entanglements

It's a reasonable question and it touches at the crux of the issue. But I have one quibble with how you state it. You shouldn't talk about a wave function doing anything. It's not necessarily a real thing except insofar as it influences a measurement.

So let's talk about measurements. You set up the entangled particles in the middle of two observers 10 million light years apart. 5 million light years later, they take their measurements. If the two measurements are separated by a spacelike interval, that is to say if light couldn't travel from one measurement to the other, then you cannot say that one measurement took place before the other. There is no universally agreed upon definition of "right now". It depends on your frame of reference. So it doesn't make any sense to say that observer A collapsed the wave function or observer B collapsed the wave function. They both took their measurements. (Actually they took many measurements of many entangled particles). They send their measurement results back to the middle where they are compared. And 5 million years later, it is found that the measurements were correlated in the way predicted by quantum mechanics. But niether A nor B, at the time of the meaurements, has any way of knowing what the other is doing or not doing.

So all this isn't really a problem unless you suppose (as Einstein did way back in the day or as Bohm did more recently) that really the particles secretly "know" what their spin is all along. If that were the case, then the particles would have to communicate faster than the speed of light to make sure they got their stories straight when the measurements are taken. But if you suppose that the particles don't really know their spin until measurement, it's not a problem.

in this case, you're asking (fundamentally) when do the quantum states collapse (by being observed). Is it instantaneous, or is there some delay? There has been a great deal of experiments done for this, and all so far (that I know of) indicate that it is indeed instantaneous. While the experiments haven't been done over light years, the current theory would expect that to also be instantaneous.

This doesn't seem to violate relativity, since you still cannot transmit information faster than the speed of light. This phenomena has interesting applications for encryption, however.