After replacing the o2 sensors (all 3 of them) my 2005 Durango idles rough and dies when you put it into gear.

first put the 02,s back in,clean or replace the EGR,IAC-Idle Air Control.as for the slipping in tranny,may be a shift sensor going bad,or worse.

I have an 2002 Durango and it ackted like that when my battery was getting weaker and I know that many of the gen 1 have had that problem. So load test your battery and check the Alternator it is so pose to give you over 14 volts. You might get away with cleaning the connectors on the battery with a wire brush or sanding paper.