Since it's just the trim and not a structural thing, liquid nails should work fine. You just need to clamp it to pull it tight, sand, wood filler to cover crack and repaint.

I would use a good quality wood carpenters glue. Squeeze it into the crack even if you need to pry it apart a bit to do it. A small paint brush works well to get the glue into the crack. Then as Leslie said you need to use a small bar clamp that will reach across both sides and clamp it tight. Some glue will come out, that is ok. It tells you that you have enough glue in the crack. Once dry sand and paint. If need be, you can putty any gaps that remain. No clamps? Then using some ...»

Get some MaxFlex caulk at the local Sherwin Williams, apply some into the crack, drive a couple of thin brads/finish nails into the face of it, smooth over the caulk in the crack, spot prime rough wood and repaint with white semi-gloss...easy fix