How cold is it at night? Can you open your bedroom windows during the day to air out your room so the smell isn't overpowering and offensive to your mum?
She is just concerned for your health and the cleanliness of her home.
If they are kept in a secure brooder and they have their heat lamp, I think they would be alright. Duckes tolerate cold much btter than heat - within reason.
If they huddle together near the heat lamp, they are chilly and maybe need a stronger bulb or the heat source a little closer to them. If they spread out far away from the heat lamp, they are too warm and need the heat a little farther away. If they are running around in between the warm and cool spots, then they are just right.
Or, if you can keep the brooder drier and not smelly, maybe your mum will let you keep them in your room another week or 2? Can you get wood shavings? Here we get them in a bale shaped plastic bag. Shavings reduce odor immensely, and can be spread under the bushes an in the flower beds or composted when you clean out the brooder to use as mulch (bonus- the mulch keeps weeds down).
Clean wet shavings out daily.
Also, you can reduce the wet mess by taking a plastic gallon jug an cutting a window in one side big enough for the ducklings to stick their heads in. fill with water and set in a large pan to collect any spills. The ducklings can wash their faces and the wet mess is reduced. Empty the spill pan daily when you change the water in the jug.
I know how hard it is to keep ducks clean as they are messy little guys, but maybe this will help you.
If mum stands firm and says no to keeping them in the house any more, you should still play with them a lot to keep them tame and focused on you. When they are left to their own entertainment, they become all duck and don't care so much bout people. So play with your ducklings daily.