Comes from the name Laundromat. Since it's you mom's house you call it Mom-dro-mat.
Can also be called Dad-dro-mat. If you go to your Dad's house.
You: I will when I get a chance.
Friend: When you get a chance? There is a laundromat right down the street.
You: No way I not paying to wash my clothes I go to my Mom's house.
Friend: Oh yeah the good ole Mom-dro-mat