洗車を終えた means finished washing the car.
車をふたりがかりで拭いているの means two people wiping the car together.
1) But I would like to know whether the subject of 洗車を終えた is 喜一? So after 喜一 finished washing the car, he watched two people wiping the car together? If not, what is the subject of 洗車を終えた?
2) This sentence looks confusing to me as if 洗車を終えた is used to modify the 車 after it so it reads like "the car that has finished washing the car". I would like to know what kind of sentence structure is this? It seems that something is missing after 洗車を終えた.