That's a difficult one. Is your mother-in-law making you take your diapers home when you are others house, but what about her house. If she's ok with it at her house, maybe someone said something to her about diapers in their garbage and she's just trying to prevent a dispute between you and the host.
When I'm at people's houses that aren't used to having babies, I grab a bag and wrap the diaper in the bag before I put it in their outside trash. I always ask where the best place with a dirty diaper would be. Most of my friends understand that it would be much better to put a dirty diaper in the outside garbage rather than bringing it back into a enclosed space like a car.
Your mother in law might have also been taught by her mother that you shouldn't leave a dirty diaper at a hosts house and she's trying to pass down what she learned to her son.
I would ask the host what they would like best (in front of mother-in-law in needed) to see where they would like the diapers or if they would prefer you took it home. Most hosts wouldn't expect you to carry the diaper back home.