RTL display only correct after empty cache?

Ok, I’ll try to explain as good as I can…

My website – indiebabie.com – is working with Artificer theme, WooCommerce and WPML. The website is in Dutch, English and Hebrew. I work on an iMac with Safari, Chrome and FireFox,

I have added a rtl.css to display the Hebrew version. In Sarafi and Chrome I have to empty cache in order to see the Hebrew site in RTL. Only then it displays correct however the dropdown below “my account” is gone. When I refresh/visit another Hebrew page everything goes back to LTR and the dropdown sometimes returns, sometimes does not.

In all three browsers page titles randomly appear either RTL or centred.

The header stays on the left no matter what I do…

As I tried all I good think of/find online, I am not sure how to fix this. It’s so frustrating that I even consider changes theme. I’d be very thankful if anyone can point me in the right direction.

Thanks!