My mom gave me her Apple Watch as it “wasn’t for her.” She did not unpair it and doesn’t live by me.

It is possible to unpair the watch without having your Mother's iPhone if you follow the steps in Unpair and erase your Apple Watch

1 On your Apple Watch, tap Settings > General > Reset > Erase All Content and Settings. 

2 Type your password if prompted.

3 For GPS + Cellular models, choose to keep or remove your cellular plan.

• If you want to pair your Apple Watch and iPhone again, keep your plan. 
• If you don't want to pair your Apple Watch and iPhone again, remove your plan. If you aren't going to pair with a different watch or iPhone, you might need to contact your carrier to cancel your cellular subscription. 

4 Tap Erase All to confirm. This resets your Apple Watch to the factory settings

Clearly this will require her consent to have you use her credentials.

For your mother;

What to do before you sell, give away or trade in your Apple Watch