I don't know if you're triggering the Inon now with fiberoptic or just 'wirelessly' (the photodetector sees the camera's flash). But regardless, the issue is going to be that the Ike doesn't have any sort of 'external auto' mode but triggering only with their fiberoptic adaptor. All control is from the dial on the back.
So if the Inon is 'wireless', once you add the Ikelite, more than likely it's the Ikelite that gets mimicked by the Inon. The Ike is going to be the brighter source so when it flashes it triggers the Inon, and when it quenches it triggers the Inon to quench. So in that case adjusting the dial on the Ike is adjusting 'both' of them sort of. I'm guessing you'd just block the on-camera flash to only what makes it thru the F.O. to make sure. (I'm probably mixing up S-TTL optical with external auto modes...I really have a hard time understanding the Inon manual I downloaded).
If the Inon is on fiberoptic to the on-camera flash as well (e.g. the photodetector doesn't really "see" the Ikelite flashing), you might get a confused result: the Inon might successfully S-TTL trigger and quench based on the on-camera flash, while the Ike only triggers but can't quench in response to the on-camera flash. Adjusting the dial on the Ikelite is only adjusting the Ikelite in this case. So while one is trying to do TTL communication with the camera, the quench command isn't being obeyed by both, and I'm guessing this might be more frustrating than the case above, where you've lost all TTL and are essentially shooting manual, but at least one adjustment is in effect adjusting both strobes.
Disclaimer: I don't and never have owned any Inons (yet). Been researching them. One friend tells me he sets one to external auto and the other adjusts manually, triggered by electrical cable to the on-camera strobe hotshoe (he's on an Ikelite housing, but with 2 Inon strobes, so the on-camera flash is down and doesn't flash, the included electronics see the hotshoe pulse but can only offer manual triggering to non-Ikelite strobes). So he can only shoot with manual strobe control, but one knob adjusts both strobes in most cases. Sort of sounds like what you'd be forced into, but with the Ike F.O. connection replacing the electrical sync manual trigger.