Header design

Hi,
I was searching for a solution in other topics, but I can’t seem to find the exact one and whatever I tried doesn’t work for my case.

Please see my website. I would like to reorganize the header as shown in the screenshot here:

When I make the logo left and menu below – the cart and search button jumps – see screenshot here: https://www.screencast.com/t/Utocjz7j5up

So, here is what I am looking for:
1. to have a shop button that I can style my way near to the cart icon and on the right side of the logo
2. in the middle between the logo and shop button – some easily editable text area, where I put news, coupons and so on.
3. The logo to be on the left and main menu below without destroying the layout”
Please help me to understand where to start with.

Thank you