I think you should try to get it to work in some other way.
It’s normal it doesn’t work, since the url from the page can’t be changed by the .htaccess, because the url is not your permalink but the new domain.
Why not set the name server of the new url, to the old one.
so they go to the same page.
Then change your .htaccess, accordingly to change to your internal wordpress link when the website is visited from the new domain. That should work.
If you don’t find how to change your .htaccess file accordingly let me know I can have a look.