Do you each have your own iPhones with separate Apple IDs? If you and your wife are sharing an Apple ID, you will continue to have these kinds of problems and there is really no work-around other than each of you getting your own Apple ID. If there is info, you want to share, use Family Sharing:
What is Family Sharing? - Apple Support
Set up Family Sharing - Apple Support
If that is not the problem, how did you setup the watches? Did you each setup your watches to your own iPhone:
Set up your Apple Watch - Apple Support
or did you use:
Set up an Apple Watch for a family member - Apple Support