Mixing Exchange email and Pop3 email

I have one Exchange email box and a master calendar for several other therapists.
We have all other emails as Pop3 email boxes.

the exchange email is info@totallifecounseling.com

Pop3 is the name of the therapist@totallifecounseling.com

When we email appointments from the calendar to one of the therapists it often gets thru fine. However, we get multiple delay messages and 4-8 nondeliverables each day.

Is there a way around this as I have been advised to convert all mailboxes to Exchange to avoid this hassle?

Several