A fast ISR is the best way to go.

But you may get away with other routes too.

For example, if you read the RTC interrupt every second to update the time and test the other things you want. Finally read the IR code.

Since IR transmission is not repeated quickly, you have plenty of time to do the above tasks. The worse that can happen is to loose one transmission but will grab the second.

I believe your RTC does have an Interrupt output, so that MCU can be triggered, either poll or by interrupt regularly.

Ioannis