Check your Management Agreement that you should have signed with the current PM at the commencement of the term. Usually most MA's require 90 days to terminate their agreement but I alter this to 30 days. After all, if a PM is confident that they are doing a good job, they shouldn't have any problem with this amount of notice.
If you're not confident in sacking the first PM, simply give the appropriate notice in writing and get the other PM to transfer all the paperwork, pick up keys etc.
Mind you, I think it's more valuable for you to leave honest feedback. Even if you only want to do it by phone, rather than in person, at least it provides an opportunity for the PM to improve her services. She may not even be aware that you are unhappy.
Good luck with it all.