trigger my relay to close

You just have to follow this simple logic, in C-ish pseudocode:

if (day_of week == Monday || day_of_week == Wednesday)
{
  if (time_of_day >= 1700 && time_of_day <= 1710)
  {
    relay_on();
  }
}

How you get the time and how you drive the relay will depend on your hardware and on the library (if any) that you'll be using for the RTC. If your relay is bistable, the logic is a bit different: you'll have to turn it on at 1700 and turn it off at 1710.

Have you written any code yet? How is it working right now?