The Metars that day were as follows

KHPN 232056Z 19014G20KT 1/4SM FG OVC002 13/13 A2947
KHPN 232018Z 19012G20KT 160V220 1/2SM -RA FG OVC002 13/13 A2948
KHPN 231956Z COR 18012G20KT 3/4SM -RA BR OVC002 13/13 A2948 RMK
AIRCRAFT MISHAP
KHPN 231856Z 19012G16KT 1/2SM FG OVC002 12/12 A2951
KHPN 231756Z 18013G19KT 1/8SM FG OVC002 12/12 A2952
KHPN 231743Z 17016G22KT 1/8SM FG OVC002 12/12 A2951 RMK AO2
KHPN 231656Z 19013KT 1/2SM FG VV002 13/13 A2952
KHPN 231556Z 18006KT 1/4SM -RA FG VV002 12/12 A2954

turns out that POU had 800 foot ceilings and 7 mile visability and DXR
had 300 and 2 mile vis.....

The most charitable thing we can say is that praciticing IFR approaches
in those conditions with a PPL student was less than optimal judgement.