Some people are more particular about it that others.
I am with you - it was easier for you to sit in the back than your mother, so you sit in the back and let her have the front.
Others would be with your husband - it is your car and she is the guest so you get your normal seat and she takes a spare.
Then others would offer the front seat to your mother for another reason - respect for your elders. She is your mother and as her daughter it is a given that you will show her respect and step aside for her.