I'm not interested in having relationships with others. But I'm ok with my wife having relationships with other women and will join in on sex. What kind of relationship would you define us as having?
Well, since I'm not one of the women your wife is hoping to date, it doesn't really matter how I'd define your relationship! I'm not the Polyamorous Sorting Hat capable of telling you exactly who and what you are.
The purpose of defining our relationships is to help us better understand them, and in turn, to help us explain them to other people. The right word for your relationship is whatever word helps you two find and cultivate healthy, fulfilling relationships, articulate your needs, and live authentically into what makes you happy.
You may find that "polyamorous" best describes your relationship; or that "open relationship" captures it better, or there may be another term that works better. You may settle on one, then realize you need to change it if people who meet you under the assumption that you're XYZ get turned off or confused or bring unhelpful assumptions to the table.
No one word will encapsulate everything about what you two need from others and have to offer, though, so be careful not to put those expectations on finding the perfect descriptor. You'll still need to be able to discuss, with clarity and honesty, who you are, what you need, and what types of relationships you're envisioning.
Consider also checking out my FAQ on this topic!