WP theme update causes child theme CSS problems

It may be possible that your theme author would be able to provide you with a previous version of the theme, not sure though. In regards to how you can avoid this issue in the future, I would recommend performing a backup of your WordPress files before updating anything (this goes for plugin updates, WordPress core updates, etc). There are a bunch of plugins out there that can help you with running automated or manual backups.

You could also set up a dev subdomain or recreate the site on a local environment and test any changes you want to make there before making them on your live site.

In any case, I would always recommend running scheduled backups of your site to ensure that you can always roll-back in case something goes wrong. In your case right now however, I would start to take a look at your child theme and fix your styling issues that are conflicting with the theme update.