should my wife and I share the same apple id and password

Hello ~ I would not recommend that. Click this helpful link by clicking below….

Make sure that each family member has a unique Apple ID - Apple Support

Post back with any further questions and I hope this helps.

~Katana-San~

Generally not a good idea. Such as any time either of you add, edit or removes a contact, it will affect both devices. Same with photos.

The wife and I have separate accounts and just let each other know what our IDs, passwords and passcodes are, just in case we need to access each other's phones.

No, an Apple ID is strictly personal, use your own one