There is no need to "explain" quantum entanglement, because it is a prediction of a theory that has been around for 80 years. So it is already "explained." The remarkable feature was that experiments verified this old prediction. Einstein had expected that experiments, when possible (but they only happened after his death) would have shown entanglement to be wrong.

The problem with entanglement is that it shows (to use Einstein's words) "spooky action at a distance." By that he meant that it requires changes in the wave functions to occur faster than the speed of light. But relativity is not violated; it turns out that you can't use this spooky action to transfer information faster than light.

Many of us are still bothered in the same way as was Einstein.

The trick, if you are going to apply a 4th dimension, is to reconcile entanglement theory with relativity. If you can use the 4th dimension to present quantum physics without using wave functions, maybe you're on to something.