Most wood adhesives rely on penetration of the glue into wood fibres. With a repair job the fibres are all sealed by the old adhesive and so wood glues are less effective. If you remove the old adhesive to get ack to open fibres then you have a loose joint.
There is a potion called Chair Doctor and this is an especially limpid glue for injection into joints where you can't get them fully apart.
My inclination would be to remove any loose material/dust etc and use Araldite epoxy which seems to stick virtually everything hard apart from glass and PTFE