Got it, thanks. Your header area is a T4 Block, which I don't tend to use, so am unsure if they can be easily edited. I will have a look later at whether it can be fixed with custom CSS. In the meantime, maybe the Mods can help, as there is clearly a display issue in mobile view.
Another option could be to put the language switcher module in separately and only display on mobile devices.
Actually, I just tried it with some quick CSS...
@media (max-width: 991px) {
.t4b-header .t4-head-mod {
position: absolute;
top: 10px;
right: 60px;
}
Makes it appear as below. It would need to be checked in some more detail though. It's not an ideal solution either, but may work ok.
I appreciate you wanted it to the right of the menu icon, but I think it looks fine to the left.