Dear Piotr,
I’ve follow a lot of way to solve it, but after 5 months from purchase i am in the same point.
I’ve payed a freelancer even to solve it, and he share some information with your staff (Hans) by email, but he (Hans) say that is a WPML issue.
But the problem was the same with Polylang! Infact if you check my first post you can see as i ask for polylang.
I have the same WPML version in others website but only with Parallel theme i have this problem.