Hello,
1. If everything is ok on dev site you can move the child theme files to your live server. If you made any changes in child theme style.css then do the backup of this file, compare dev and main files https://text-compare.com/ and add your changes to dev file.
2. Once you move the dev child theme files to change the carousel, contact us again and we’ll check what it the reason of your issue.
3. What options do you suggest?
Regards