Hi Accademia45645! Round Robin Event Types will not ever allow for intentionally selecting a host in the booking flow. This is because Round Robin ETs are designed to fairly distribute bookings to multiple teammates (hosts). However, you have found a decent workaround in rescheduling and selecting a host, that way.

However, bookings cannot be auto-moved from one host to another. If an invitee reschedules, they will be shown times that the original host is available for rescheduling. Otherwise, you’d need to cancel that invitee entirely and book them with the alternative host. If this is not the case my guess is that the person rescheduling is using the original link rather than the “reschedule” option. You may want to reach out to our Support Team for this as they will be able to walk you through your setting live → Support - Contact Us