Is this The Cape Canaveral Monsters (1960)...?
When a couple are killed in an auto accident their bodies are immediately inhabited by extraterrestrial beings. Taking refuge in an underground cave, the aliens attempt to sabotage the U. S. space program.
This is a black & white film. Right at the beginning, two aliens appear on a beach on Earth, looking for "suitable bodies." At this point, they have no physical form and are depicted as a couple of tennis ball-sized balls of energy.
Unaware of the aliens' presence, a man and woman are relaxing on the beach, then pack up to leave in their car. The aliens float into their car unseen and enter their bodies while the car is in motion. The car crashes, killing both of the human hosts the aliens are now in possession of. The aliens retain full control of the bodies, but the man's left arm was completely severed in the crash. They leave the car on foot, and the one in the female body takes the severed arm with her, saying she'll sew it back on later.
This all occurs within the first three minutes of the film. About six minutes deeper into the runtime (hours later in the story), the alien in the male body has his left arm torn off again by guard dogs, while sneaking around at Cape Canaveral. After that, the alien in the female body concludes that they'll need to replace the missing arm with a living one.
I didn't see a part where she scolded him about human bodies being fragile. She does speak to him with disdain at times though, and vice versa.