I have installed a single toggle switch/outlet on a GFCI circuit and the outlet is fine, however, the toggle switch for 3 recessed led lights trips the GFCI.
The circuit as you have designed it will not work. You have routed current from the load hot terminal of the GFCI through the switch and load, then back to the neutral node in your service panel, bypassing the load neutral terminal of the GFCI. The GFCI senses this imbalance and trips.
You cannot mix a GFCI protected path with an unprotected path. You must either power the toggle switch and LED load completely from the GFCI load terminals, like this:
or power the toggle switch and LED load completely from the unprotected mains supply, like this:
One path or another will require a 12/4 w/g instead of a 12/3 w/g cable.
Did you hook the neutral to the switch instead of splicing it to the one going to the lights. Power in,power out of switch. Neutrals butt spliced and then properly grounded bare wires.