Hi Janneke!
Thanks for getting in touch with us. Let me help you with that issue.
Please, let me first note that the order property is not supported by the tribe_events shortcode. I don’t think this could be an issue here, but just wanted to let you know about it.
It seems strange to me that those two events you mention do not show the year they are in. Could you please edit those events and see that their start/end dates are correctly set? If so, please try editing and just saving it again to see if any difference.
If nothing changes, then there is a chance this could be a conflict with a theme or plugin, so to narrow the problem down please go through the steps provided in the testing for conflicts guide > https://theeventscalendar.com/knowledgebase/testing-for-conflicts/ and let us know what you find in the process. I know you already tried disabling all other plugins, but do you notice a difference using a default theme?
I suggest to setup a dev/staging site so you can test things out and make all plugins, theme and WordPress core updates without disrupting the live site.
Please let me know how that goes.
Thanks,
Victor