If you are using the same colour space for the two displays, PSE should not be the cause of different colour rendition between the two. Yes, a laptop display can be calibrated and profiled, but that is no guarantee the results will be any good. Just keep your head still and flip the lid back and forth a bit. You'll see what I mean. Good profiling should make the same image look about the same on two different stand alone displays. But it's not foolproof especially when it comes to laptops, and you are using different profiling packages and software for each display - I'm guessing this could produce differing results, but that's not what colour management is supposed to be doing to us, so I'm a bit mystified on that one. If you can profile both displays with the same package and see what happens, that may be instructive.
There are separate digital asset management programs available (for example ACDSee) which would allow you to organize your stuff and work it with PSE.