Website was created on incorrect URL. Database, Wordpress settings and all plugins must be re-set to correct URL. Neither database nor site files need to be moved. You should, however, perform a full backup before doing the work. Site has several plugins pointing to the old URL.
Note - work must be done on a Saturday morning Pacific Time to minimize downtime. After you make URL changes, the site will be down, so it's important that the last settings changed be the WP main settings, and database. I will transfer domain to the correct DNS and move email addresses after you are done with your work.
In case of coding errors, you must be available to respond by email during the course of the DNS propagation. If you're located many hours ahead of me (like India, for example), response within 5 hours is ok.