Keep in mind that the comment was that "looking at others' photos between the two laptops yield very little difference, however my own images look visibly different between the same 2 laptops"...
That is the fly in the ointment so to speak. If it was simply an issue that there are 2 different laptops, one calibrated and one not, and all images are different between those two laptops, then the solution is pretty obvious. However if the aforementioned statement is correct, then the cause is more difficult to solve, yes?
Maybe - but one issue is not knowing the content of the images and how they were produced. Because there are no examples of any (either the images that are good, or ones that are not good in terms of their appearance) it is not possible to start addressing the issue.