Accidentally connected Mom’s iPad to mine

Check the AppleID being used by each iPad for iMessage:

Settings > Messages > Send & Receive > [Start New Conversations From] AppleID

If your own AppleID is not shown on your iPad, or your mother’s AppleID shown on her iPad, tap the AppleID (shown in blue text) on the iPad that is incorrect - then select Sign Out.

Next, restart the iPad:

Settings > General > Shut Down

Restart the iPad using the Sleep/Wake button - then sign-in to the correct AppleID on the affected iPad:

Settings > Messages > [Send & Receive] AppleID

you can take these steps and make a do over

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

In what manner do you believe that you have “connected” your own and your Mother’s iPad? Are they signed-in to iCloud with the same or different AppleID?

The more information that you can provide, the more likely contributors will be able to provide appropriate help or guidance.

Writing an effective Apple Support Commun… - Apple Community

Without more information, it is impossible to provide any guidance that might not cause loss of data.

Accidentally how?

What did you do?

Having Family Sharing does not connect devices to each other.

You will need to explain exactly what happened, and what you were doing before it happened, before we can provide any help.