apple watch

What I would do is unpair the Watch from your iPhone, set up your iPhone with the new Apple ID, then pair the Watch to your phone. If you have an Apple Store near you that is open you might want to make a Genius Bar appointment to get some assistance with this: Genius Bar Reservation and Apple Support Options - Apple

Create your own Apple ID then set up Family Sharing.

How to create a new Apple ID - Apple Support

Set up Family Sharing - Apple Support

As you have seen, sharing an Apple ID is a bad move, especially with multiple devices like you have. Someone has to create a new one, then Family Sharing works great. Our family has been using it for a while. It is great.

Are you sharing an Apple ID? Is the Watch activated with your husband's Apple ID? Do you have Calls on Other Devices turned on in your iPhone and is your husband's phone selected there?

Make sure your iPhone and Watch is using your new Apple ID and then set up family sharing using the second link I provided.