Hello and welcome to Apple Support Communities, weapon90.
If I understand your post correctly, you and your wife are trying to share your Activity from your Apple Watch and hers. I’d like to help.
Follow the steps in this article:
Get help with Activity Sharing
To compete with friends, you need iOS 12 and watchOS 5 or later. Activity Sharing requires iOS 10 and watchOS 3 or later.
If you paired more than one Apple Watch to your iPhone, the Sharing tab won't appear in Activity until you update all your watches to the latest version of watchOS.
If you see an error when you try to add a friend or send an invitation
Sign out of iCloud on your iPhone, then sign back in:
Tap Settings > [your name].
Scroll down and tap Sign Out.
Go back to Settings > Sign in to your [device], then enter your Apple ID and password.
Tap Sign In.
Try to add your friend or look for the invitation.
If you still can’t add a friend, make sure that they have an Apple Watch and that you haven’t added the maximum number of friends. You can add up to 40 friends.
See the full article here:
Share your Activity and compete with friends with your Apple Watch
You mentioned that when you send the invitation you are both able to see that it was sent but neither of you receive it. If you are still unable to share let us know if you are each using your own Apple ID.
Thanks for using the Apple Support Communities. Take care.