Irule redirection from public to private url

, Yes you can redirect but it will create problem from internet. As if someone is trying to access https://www.xyz.com/mysite from internet, iRule will redirect it to https://wwww.abc.com/mysite and as this URL is only private URL. So, on public internet, it won't resolve any IP address. Redirection will happen but the content wont load. If you want to do such redirection from internet, first externalize/publish abc.com private URL over the internet so it will be accessible on internet too then set required redirection.

Within Intranet/LAN, the abc.com will load as expected and so redirection from xyz.com to abc.com will happen and required page will get load as expected.