You can erase the Watch completely then pair it to your mom's iPhone
Simple erase without phone
Put your watch on its charger and keep it there until you complete these steps. (select the watch OS version)
Erase Apple Watch – Apple Support (UK)
Erasing all content and settings this way erases all media, data, and settings from your Apple Watch, but it does not remove Activation Lock if it has one.
Or if it is already under your iCloud account you can erase and remove it from your account in Find My or https://icloud.com/find .
Wait for the process to finish, then set up your Apple Watch in Family setup
Read the following link, which explains how to set up Apple Watch using Family Setup to your iPhone -->
Set up Apple Watch for a family member - Apple Support