Understand where you are coming from with the original version, but the structure needs tweaking. Currently reads as… both sets of data will be isolated, but isolation will happen together, like two people in a room separated from everyone else.
with yours always implies a connection, from yours is correct.
Or, for a condensed version (less is more), consider?
Share your computer with others? To isolate data, set up each user with their own unique profile.
Know what you mean about over-thinking sentence structure. Sometimes can’t see the wood for the trees.