You cannot have two totally separate data sets , the Location data is all one.
You can use categories and use the Shortcode on one page “only_with-_category = “xx:” as shown in the link to the shortcodes I shared. and then either another short code on another page, or the category button bar or horiz checkbox..
I do not understand why you cannot use categories to separate your locations into two differentiating locations using something like the taxonomy functionality .
Or you can use the Directory landing page shortcode to work around your issue.
You might be able to do something like that with two different embed scripts if you had two separate Professional or Enterprise accounts in MYSLP and then use the two different embeds (one per page) …but since I am not really sure what it is you need to do due to the privacy factor you mentioned I am not sure how to advise you. If you need to , please send in the details of what you are trying to do to the support team or contact us and I will try to get the developer to look at your unique circumstances.