Heh. Ah the joy of people proof caps. I’ve got a couple of these and they are kind of annoying. Luckily they showed me at the
vape store. Apparently it was a common problem.
What you’ve actually done is take the cap apart. It’s a “push down while turning” system. The vanes in the underside of the outer bit fit into slots on the top side of the inner bit allowing you to turn the cap. If you remove the top half, which you have done, it becomes a somewhat slippery standard screw off cap. I actually do this as a matter of course because the two part system is so annoying to use. So basically since you’ve got the top half off just grip really hard and turn.
If that doesn’t work you can try putting the top half back on to use as a wrench.
Hope that helped. GL