Reusing domain in multisite

Good day ??

I have a WP Multisite in which a site was running. The administrators decided they would revamp the site, and they did it in a provisional subdirectory so that the original site would be available while the changes took place. So this is the structure:

– mymultisite.com
— mysite.com
— mymultisite.com/mysitebeingremade

Now that the site changes have been finished, I would like to attach the domain name to the revamped site. So, I try to disable the site currently attached to mysite.com, change its domain to a different one, and attach the domain name to the revamped one. So from the sites configuration I make the following changes in Sites > Edit site > Site info:

– mymultisite.com
— mysite.com -> mymultisite.com/mysite
— mymultisite.com/mysitebeingremade -> mysite.com

But it seems as if the domain name keeps pointing to the old site. What am I doing wrong? Or is it just impossible to reuse a domain name previously used in a multisite, but not in use anymore, for a new site?

I guess that I can just overwrite the original sites with the one with the changes, but I think it is too much hassle for a seemingly simple task.

Thank you ??