help making a header using all my code instead of the wordpress header function

[designsbymkp]

Im sorry if this is a stupid question, but I am getting a huge headache working on this responsive design, I am new to these and my client is being very specific with their needs. The only way I can imagine getting the header like I want, is to just use my own code for the header, but can not figure out how. Is there somehow I can use my own code for the header than using the custom header function and the right header widget box? The widget box works great for the right side, but the site title which I want to be an image is just not working right for the responsive design I need.
Here is my first go on the website using a child theme (it is really rough so please do not judge) and the header just does not work right when you make the screen smaller.
www.mkpdesigns.net/atlanticglass/
And here is my second go (which is even more rough and in progress) which the right part is working better, but the left part of header, the logo, is just not working like I want. The only way I can imagine getting it to work right is just writing the code like I did in the header right widget.
www.mkpdesigns.net/ag-decor/
Is there anything I can do? I am sorry if this is the wrong forum to post in, really not sure, but I appreciate any help!!!