The hoses poping off of the DPFE sounds like something is causing you to have high back pressure.
I don't know how that would happen suddenly.....but maybe this has been the problem all along?.
Did you change the DPFE, or for some other reason remove those hoses?
The DPFE would not be causing the excessive pressure in any way.
The DPFE senses the difference in pressure between the 2 hoses.
There is a restriction in the EGR tube, between the 2 hose locations on the tube.
With the EGR valve closed, as is normal at idle, there would be no flow through the tube, and no difference in pressure between the 2 locations.
With the EGR valve open, there will be a slight difference in pressure between the 2 locations with slight airflow through the EGR tube.
The EGR tube will be at whatever pressure the exhaust manifold is at.
A defective DPFE, EGR valve, or EGR tube is not going to change the fact that the hose in question is going to be at about whatever pressure is present in the exhaust manifold.
The PCM (computer) should not be asking for the EGR valve to be open while the motor is at idle.
You could check this by removing the vaccum line to the EGR valve and seeing if the idle improves.
It is normal for there to be a slight amount of vaccum in this vaccum line at idle....but not enough to open the EGR valve.
It is sounding like you have excessive pressure in the exhaust manifold.
While the DPFE may or may not be defective, I do not see it causing this excessive pressure.
I would say that you need to solve the back pressure issue first.....and see if that solves all the problems.