Hi @DanDan!
You might be running into some conflicts with mixed content or caching when previewing. When you move the site to your live host if you’re using Local Connect or a migration plugin there will be search and replace tasks and cache flushes happening automatically.
More about troubleshooting this here: Troubleshooting Live Links
For Elementor specifically, you might need to Regenerate CSS. They also have a S/R tool I believe as well. Here is a recent comment of mine with some more tips: