If the elements are always double quoted, then you can replace quote-space-quote with quote-newline-quote:

$ sed 's/" "/"\n"/g' <<< "$variable"
"/home/myuser/example of name with spaces"
"/home/myuser/another example with spaces/myfile"

But it would be simpler if you can modify your script to use an array:

$ vararray=("/home/myuser/example of name with spaces" "/home/myuser/another example with spaces/myfile")
$ printf '"%s"\n' "${vararray[@]}"
"/home/myuser/example of name with spaces"
"/home/myuser/another example with spaces/myfile"

If the elements are always double quoted, then you can replace quote-space-quote with quote-newline-quote:

$ sed 's/" "/"\n"/g' <<< "$variable"
"/home/myuser/example of name with spaces"
"/home/myuser/another example with spaces/myfile"

or (using shell parameter substitution)

$ printf '%s\n' "${variable//\" \"/\"$'\n'\"}"
"/home/myuser/example of name with spaces"
"/home/myuser/another example with spaces/myfile"

But it would be simpler if you can modify your script to use an array:

$ vararray=("/home/myuser/example of name with spaces" "/home/myuser/another example with spaces/myfile")
$ printf '"%s"\n' "${vararray[@]}"
"/home/myuser/example of name with spaces"
"/home/myuser/another example with spaces/myfile"