If you want to switch from, for example, a monthly to an annual subscription, you do this on the subscription owner's app via Settings > Subscription > Manage subscription, after which you will be guided to the App Store - Apple or Google Play Store settings respectively, depending on whether you have an iPhone or Android.
If you want to cancel your subscription, this is also done on the subscription owner's app through Settings > Subscription > Manage subscription, after which you will be guided to the App Store - Apple or Google Play Store settings, respectively, depending on whether you have an iPhone or Android. Please note that all family members linked to the family will lose access to the app, but all history will be saved if you wish to subscribe again. Also be aware that if you have the MyMonii Visa card, this will no longer be usable if you cancel your subscription.