Oops. Too much to take :o)
One thing though: An excellent mix (EM for short) done with excellent soudcard and excellent loudspeakers can be called excellent only if it translates to other systems. That's the whole point! If the EM sounds bad on some other soundsystem it's useless, it is NOT a good mix then. You realise that all commercial CDs can be thrown in any player and they sound OK or great depending on the system. That's how the mix must be. Any speculation you seem to like :o) doesn't lead anywhere.
Every soundsystem sounds different, and an EM sounds good everywhere (in relation to the quality of the soundsystem).
One of the key things of your problem setting is that you don't compare how the wav sounds through the integrated soundcard of laptop #1 and #2. Most likely it's almost the same.
I did not mean that you are surprised by the quality difference of the laptop speakers. It was a comment to your statement, where you said that people are.
Roey Izhakis book "Mixing Audio" is good read in developing your mixing skills.
You're not alone. It's hard for many beginners to believe that a mix that sounds good by the studio working spot is absolutely useless in other surroundings. One good way to learn is to import a commercial track on one track of your project and compare the sounds and frequency curves.
OP= Original Post