Apple Watch will not connect to my phone for a family member

Make sure that you have an eligible cellular service plan with a supported carrier. Your iPhone and Apple Watch must use the same carrier, and you must be within your carrier's network when you set up cellular on your watch. nCarriers in the US typically charge an extra $10 monthly for the watch in addition to the iPhone. For more info, see:

Set up an Apple Watch for a family member - Apple Support

Set up cellular on Apple Watch - Apple Support

Apple Watch - Carriers - Apple