Can my iPhone and my child’s be on the same AppleCare one plan?

AppleCare - Apple

Can I add my family’s devices to my AppleCare One plan?

AppleCare One plans can cover devices that are on the same Apple Account as the subscriber.

Apple does not like to use the word “no” in its documentation but the above statement effectively states that all devices have to be signed into the same Apple Account. You cannot have another family member’s device under your AppleCare One plan unless they are sharing an Apple Account with you (which Apple in turn strongly recommends against).

The current AppleCare One program does not have a Family Sharing option.

Not much is known about AppleCare One at the moment, but if both you and your daughter’s account on Family Sharing, most Apple subscriptions will share over to other family member’s devices if permitted. I’d say go for purchasing it for one month and seeing if it works. If not, unsubscribe and remain on the AppleCare+ plans. However, AppleCare One might still be a good addition if you’re looking to extend coverage to all of your devices.