And entry can be assigned to more than a single category. So, you can assign an entry to cat1 and show. That entry would still display on the page which displays cat1 and since it is also cat show, it will be open by default. Similarly is entry2 is assign both cat2 and show, it will still be displayed on the second page for cat2 and will be open by default.
I suggest giving a quick try on two entries in two different categories to make sure this solution does or does not meet you needs.
Hope this helps!