Hello Aaron,
I think that you can use family sharing to sort this out. First thing is to decide which Apple ID will become the head of the family, yours or your wife's Apple ID. Any future purchases will be applied against the payment method linked to this ID.
Set up Family Sharing on a device that's signed in to the main ID by following these steps:
https://support.apple.com/en-gb/HT201088
Use the steps further down on that page to add the other ID to the same family. Once you've done this, you should be able to download each other's iTunes purchases, if needed, see here:
https://support.apple.com/en-us/HT201085
If you run into problems with this, consider calling Apple support, they're really helpful and will usually help you out with this during a phone call.