"I go to my mother's every week."
Translation:Jeżdżę do mojej mamy co tydzień.
In English mother's indicates that you most likely mean your mother's house but I think it's correct without the 's here. In Polish we don't generally make the grammar distinction. Here are some useful expressions:
to my mother('s) = do mojej mamy (do + genitive)
at my mother's = u mojej mamy (u + genitive)
OK, "każdego tygodnia" seems fine, so added.
One thing though: as the Polish sentence had "mamy", I made "mom" the default English version, and therefore "matki" became too formal to be the backtranslation.