To unpack your question - you are asking about Reminders app entries visible in your Calendar app?
I am not clear about what you mean by 'assigning' reminders. The meaning I take from that is that while these are shared reminders they are labelled for action by one person, yet visible to both because they are in a shared List.
Reminders can be shared or kept to your own device. Your question tells me that you want some reminders shared and others kept to your own devices. Sharing is done by sharing a group of reminders called a List, and this is what you are doing in sharing with your wife.
For reminders you want on your device only, and not unnecessarily appearing on your wife's iPhone, you will need to create a new list and then populate that list with reminders. These will be active on your iPhone only - or to be more accurate devices signed into your iCloud account. A further step is required in order to share this new Reminders app List.