There might be law to allow tenants to live there for some time, but I don't believe there is law to keep the PM. If you're not happy with the guy, just negotiate with the tenant. As long as you can show you're the new owner, and they are OK with a new lease, I'm guessing you should be able to bypass the PM.
But first you need to get the prior lease. If you could keep the family there, then you are saving on the repairs you probably need to do in case they move out and you have to find new tenants.
This is my guess, though. Check with your own legal counsel.