I see your flicker photos now. Unless you are handy with wood working, I would be careful about taking the door apart. I would myself but I have tools and bits to that to make a rail and stile door if I had to build a new one. Wood glue can be stronger than the wood itself and you can without notice, splinter that door along the grain. I personally would take the door off and clamp it down so it doesn't move and take a narrow wood chisel and carefully clean out the mortise, then take some fine sand paper and smooth out the tenon side. Its not going back together ,simply because of old dried glue in the joint. Make sure that before you apply glue back into that joint that you do a dry fit first. If it is properly cleaned, it will come back open so you can add the glue when the fit is right. Also I would put a short brad nail from the inside of the door. If you have other loose joints on the cabinet, I would tack them also from the inside. You can also get a needle type applicator at a wood working store that will inject a little glue into a loose joint and then clamp
