Is "моей мамы" genitive because of для?
The same as persian. We call overcoat "Palto" in Iran.
Palto also reminding me of the Greek word for coat
Also the Roumanian "Palton"
Based on the preceding sentences, why not для своей мамы or even just для мамы?
Luckily in Russia there aren't any English weather conditions or dressing problems:-)
Palto very close to how it's said in romanian, palton