Hi,
What you are looking for is called responsive design, where website html and css is done in such a way that it fits with all kind of devices mobile, tab and computers/laptops.
But what I see, you already have a responsive site, which accommodates itself, but definitely there are issue not working properly.
I have couple of question :
Are you looking for mobile version of website separately done outside of responsive. So that when people open the site in big screen, it will open the desktop website and mobile compatible website when the website is opened in mobile device.
or
Do you want the issues to be fixed, which are there in your current website?
Looking forward to hear back from you. Please have a discussion with us. We will definitely give you a good deal.
Thanks
Sreemoyee.