Website Redesign Decision Support: Patch or Start Over?

In a 1-hour screenshare, I’d like an experienced web developer to review our nonprofit website’s recent redev and its responsiveness issues (content breaking across different screen sizes) and provide an expert recommendation on whether we should pursue targeted fixes (“patch”) or plan for a rebuild/redesign (“start over”). I’m looking for guidance and next-step recommendations only—no implementation during the call.

Background: Zoho Sites offered our nonprofit a massive discount to build us a new site, which they delivered and handed over. It looks nice, until you scroll or change browser size. Or if you happen to have any number of common devices. It's worst on mobile. It was distracting enough that we never actually connected our domain to it. The company says it's our issue, and if we would only find the magical combination of characters and words, this wouldn't happen.

So I'm looking for an honest, 3rd party assessment of the issue to help guide our decision on next steps!