What I want to do is just make a copy of a couple of Sim families to move to another neighborhood. I don't just want to completely remove the families from one neighborhood into another, so I thought if it would be safe if I just copy the families' files and paste them into the new neighborhood file folders (or upload through thesims2.com), or could that also mess up the game by having two copies of the same families but in different neighborhoods? (preferably I'd like to retain skills, job levels, relationships etc; I have/ used SimPE before)
I wanted to play the families like in a parallel universe type thing, just to see how differently I can play them...if that makes sense.
You do not need to remove sims from your original neighborhood in order to copy them to a new neighborhood. Since the first step in the "Hard Way" is to backup your original neighborhood, you can just restore from your backup at the end of the process and your families will still be there.
Exactly which files do you intend to copy and paste? The packages from the Characters folder? That won't work at all. You'd also need all of the appropriate records from your neighborhood package, which would be a tedious and error-prone procedure. You are much better off using one of the techniques from the linked tutorial.
Your best option is to extract your sim's appearances and re-create your families from scratch... the "Easy Way". This method is completely safe.
If you decide to use the "Hard Way", you should be aware that the resulting lot may be corrupt. That's because SimPE doesn't allow you to edit all of the records which contain references to sims. Because of this, it's very important to clean the family as well as you can, package the occupied lot, then install the lot into a test neighborhood and try playing it for a while, looking for signs of corruption. Even if you don't see any signs of corruption, you should be aware that you may corrupt your new neighborhood by installing the lot, so be sure to keep the backup of your new neighborhood. If you'd like, the HoodChecker (see my profile) may be a useful tool for further checking your test neighborhood for signs of corruption.
You just need to be aware that there is no way to guarantee that an occupied lot is safe.