How do I stop two iPhones from syncing with the same Apple ID?

Follow the steps in this article, to delete this iPhone from your Apple ID account, erase it and set it up with your wife's Apple ID:

What to do before you sell, give away, or trade in your iPhone or iPad - Apple Support

Disable "Find my" on your wife's iPhone and then remove this iPhone from the list of your trusted devices.

Have a look at this article:

Check your Apple ID device list to find where you're signed in - Apple Support

After that your wife can set up her iPhone with the newly created Apple ID:

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1. Turn on and unlock the device. 
2. If the passcode Lock Screen or the Home Screen appears, the device hasn't been erased. Ask the seller to follow the steps below to completely erase the device. Don't take ownership of any used iPhone, iPad, or iPod touch until it's been erased.
3. Begin the device setup process.
4. If you're asked for the previous owner’s Apple ID and password, the device is still linked to their account. Hand the device back to the seller and ask them to enter their password. If the previous owner isn't present, contact them as soon as possible and ask them to use a browser to remove the device from their account. Don't take ownership of any used iPhone, iPad, or iPod touch until it has been removed from the previous owner’s account.

A device is ready for you to use when you see the Hello screen.

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copied from: Activation Lock for iPhone and iPad - Apple Support

With respect, if you do not set up your wife's iPhone as a new device, but restore your wife's iPhone from your backup, all your settings will be installed again, including the Apple ID that has been used at the time of the backup.

And all apps and other content from Apple will be tied to your Apple ID as well. Meaning, if she is updating or downloading those apps again, she will have to put in your Apple ID information into the download dialog.

Setting an iPhone up "as new device" will give it a fresh start, no matter if it is used or brand-new.

You can share apps and other content you bought in the past, by setting up Family Sharing:

Set up Family Sharing - Apple Support

You could try to add an account in Settings/Contacts, as suggested in this discussion:

Contact Sharing Family

Or export the contacts from your iCloud account and import all needed contacts, using her iCloud account, via iCloud on the computer.

Import, export, or print contacts on iCloud.com - Apple Support

You can also transfer other iCloud data to a computer:

Archive or make copies of the information you store in iCloud - Apple Support

If your iPhone has the Apple ID Mail Address of your wife listed in Settings/Your Name/Apple ID, scroll down that screen and log out.

The log in again with your Apple ID.

But you still have to disable "Find my" on your wife's device, so that it can be set up with her own, different Apple ID, that is not one of your Apple IDs.

Did you try to send the invitation via mail instead of messages?

Set up Family Sharing - Apple Support

no in my phone 2 iclouds, but not my, anyone if can halome?