Is preventing one's wife from visiting her family weekly—after a prior agreement to that effect—considered a breach of the marriage contract, given that non-periodic visits are allowed?

You should not have promised something difficult to fulfill. Your breach of the condition does not affect the validity of the marriage. Scholars have differed regarding the binding nature of such conditions. The majority of scholars hold that they are not binding, while the Hanbalis hold that they are binding, and this is the view we issue fatwas according to. Therefore, your wife has the right to seek divorce if you do not fulfill the condition. It is advisable to try to convince your wife and her family to waive this condition.