Displaying blogs in a random order


I have been asked to produce a wordpress website for a Trade Association in a local village.

They want listings of every business in the village by category, i.e., shopping accomodation, restaurants, etc.

There will be 2 types of listings. The first will be for association members and will include a picture and a write up. The second type will be for non members and will only include contact details.

Now to ensure fairness, they want to display the listings in a random order each time a page is visited, therefore a different restaurant will show as the first listing each time.

My problem lies in that they want to show the members listings first in a random order, then the non-members, again in a random order.

I have sent an example of what is happening in the attached screenshot. I have the listings in their own blog, which appear in the category page in a random order, but both the members and non-members are mixed. I have separated the listings for category 'Shopping' by having the members listing in category 'Shopping 1' and the non-members listings in category 'Shopping 2'. Both of these are sub-categories of the category 'Shopping', which is my menu item.

Is there a way of displaying the blogs so category 'Shopping 1' is displayed first in a random order on the page and then the blogs in 'Shopping 2' in a random order.

Hope this makes sense?

Thank you,