"Two geese live with a grandmother."
Translation:Zwei Gänse leben bei einer Großmutter.
Well, it's a strange sentence anyway so I'm not sure my argument applies, but here is the usual explanation:
mit jemandem wohnen means that you are really sharing your life with someone. Maybe a partner, or maybe your parents if you're still a child. Maybe your parents aren't around and your aunt raises you. Maybe you live in a really cool shared apartment with your three closest friends.
bei jemandem wohnen is a bit more emotionally distant. It acknowledges that you live under the same roof but lead a more independent existence.
In the example of geese living with a grandmother both are weird, but mit einer Großmutter wohnen would perhaps be even more in the realm of fantasy.