"My mother goes into her house."
Translation:Meine Mutter geht in ihr Haus.
Akkusativ (implies directionality). As in - she goes in this direction. When it is not a direction, but a very specific object (e.g. you are looking at the house and want to say you want to go in it), then it is Dativ. This is why Germans say "ich gehe in die schule" and Austrians "ich gehe in der schule".