Go into the network admin screen. Then edit the 2nd site. Change the URL (in several places) to the www.seconddomain.com name.
Since that screen is essentially the wp-options table, there may be other places where you have to change the URL. Plus the need to change the URLs for all media files.
To do that most easily, use a search/replace plugin (I like Better Search and Replace) on that 2nd domain (via it’s Dashboard) to replace the old URL with the new URL. Be careful about what tables you specify – they should only be the tables for the second site.
And, of course, a good backup of the multi-site before you do all this is always a good idea.
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