Push to Live Host site

I’ve been experiencing an issue with broken Fonts on site my agency manages. To try and resolve the issue, I corrected it in local and tried to push the rebuild up to the live site. When I attempted this, I first tried it by creating a new site on my agency’s reseller account, and pushing the build to a new site worked perfectly, not a single hitch… however, when I then tried to push from Local to the existing live site, the font was completely broken site-wide. Originally, the font issue only seemed to occur on specific sections and modules. Now, here’s the variables in the situation. The live site, redmedclinic.com, was built with the Divi theme by Elegant Themes, we are using a child theme, there is also a custom stlye.css associated with the child theme. I did not write this style.css, nor am I the original designer of the site. My main concern is why the push from Local was seamless and successful when pushing to a site created during the push, however, the push to the existing site(with all the variables listed) did not retain the custom font I applied during my Local redesign.