Hello, I am considering buying my daughter an Apple Watch cellular. Can this be used with the mobile provider ID mobile? Or is it non compatible? Thank you.

If you daughter also has an iPhone 6s or newer, and she has it glued to her person, then the GPS only models will do everything the cellular model will do as long as the iPhone is nearby.

The Cellular + GPS Apple Watch shares the iPhone's phone number, and the carriers that support the Apple Watch charge a monthly fee. In the U.S. the fee is $10 per month. Here is a list of carriers that support the Apple Watch:

https://www.apple.com/watch/cellular

There is also Apple Watch Family Plan, if you or your spouse is using a carrier that supports the Apple Watch and the Family Plan.

You can use Apple Watch Family plan and treat your Apple Watch as if it belongs to a dependent child, which gets its own phone line, but your Wife is in charge of your Apple Watch, and because it is considered a dependent child's Apple Watch, it has limited capabilities, as the dependent child should not have access to iPhone features that a normal iPhone/Apple Watch pairing enjoys.

Apple extends the Apple Watch experience to the entire family

https://www.apple.com/newsroom/2020/09/apple-extends-the-apple-watch-experience-to-the-entire-family/

Set up an Apple Watch for a family member

https://support.apple.com/en-us/HT211768

In the UK the providers that support the cellular watch are Vodaphone,O2 and EE.