Hello,
I can give you some information, but for the most part we cannot help complete customizations like this.
I do not know what you are doing to create a member site, but you could follow our themer’s guide:
https://theeventscalendar.com/support/documentation/events-calendar-themers-guide/
And then modify this template:
\the-events-calendar\views\default-template.php
After moving that template to your theme you could wrap the coding in the check for membership so events only show that way.
Let me know if you have any follow up questions.
Thanks