Changing the WordPress Address (URL) and Site Address (URL) will not work and will probably break your website (white screen of death). Since website1.com and website2.com are essentially two separate sites what you need to do is migrate the development site over to the production server. If for example, you need to move website2.com to where website1.com is being hosted, then you’ll need to not only move all the files over from the website2.com server to the website1.com server, but you’ll also need to update all the URL instances of website2.com in the database and replace them with website1.com.

There are plugins that make this easy. I’ve had success with the premium BackupBuddy. It is a paid, but well worth it. Some other free alternatives are the Duplicator plugin and the All-in-One WP Migration plugin.

Here are some useful tutorials using the two free plugins I mentioned above:

– Move a WordPress Site with the Duplicator Plugin (https://wpshout.com/quick-guides/move-a-wordpress-site-with-the-duplicator-plugin/)
– How to Migrate your Site with All-in-One WP Migration (https://wpshout.com/quick-guides/all-in-one-wp-migration/)

I hope this helps. Cheers.