Stop enabling the delay tactics. I think this child taking advantage of you both.
I not having a 2 year old who need coaxing or bribing to leave end of day. I certain not permitting him stay when parent there until he decide good and ready. Two adult present yet two year old running the show.
Set clear expectation of child so he know what expected. When parent come, you go home. If need be, have shoe and coat on ready so can open door and push him out to waiting parent.