I don't care who recommended it to you - the relay card (as supplied) is not compatible with the RPi so the recommendation is lousy. If you are unwilling to modify it, you need a relay card compatible with the 3.3V logic of an RPi, or to use some adapter electronics between the GPIO lines and the relay card inputs.
Modified (ie by shorting out the LEDs in the input circuit), you can run it compatibly by connecting the COM pin to 3.3V. It's irrelevant that you have fitted something else to obscure access to the pin, you have to work around that.
My article "Beginners Guide to Wiring Things to the GPIO
" explains exactly what you can and cannot do when connecting things to the RPi, otherwise you should expect things not to work properly (at best), or not work at all, or damage the RPi.
As a general comment: using an opto-isolator on the drive to a relay coil is overkill. Relays are, by their very nature, isolated already.
I'm not sure why you nicked my diagram for your post, it serves no purpose and you certainly shouldn't have used it without crediting where it came from.