Hi Simo,

Unfortunately it is technically not possible to change the position of that button, this requires code customization of the template file. Code customizations are not covered by theme support.

There is only one way to show a button on a different position within the header but it is a different approach. What you can do for example is adding a "QT: Button" widget to the header panel under Appearance -> Widgets and then hide that button for desktop screens only by adding the following CSS to Appearance -> Customize -> Additional CSS:

@media (min-width:992px) {
    .header-widgets .widget-cta-button { display: none; }
    .header-widgets .widget:nth-last-child(2) { margin-right: 0; }
}