This is going to be problematic. If your ex won't share his Apple Account with her, you need to set up the new phone with her own Apple ID and start all over again. Chances are what is most important to your daughter are the photos on her iPhone. You can connect the old phone to your computer and transfer the photos to your or her computer, then they can synced to the new iPhone using these directions --> Transfer photos and videos from your iPhone or iPad to your Mac or PC - Apple Support
Then use this link to learn how to sync the photos to her iPhone after it has been set up as a new device --> Sync your photos manually using the Finder - Apple Support
She'll need to download apps all over again from the App Store, but you can establish Family Sharing to share content with her --> Family Sharing - Apple Keep in mind that apps are forever tied to the Apple Account they were downloaded under. To move the apps on her phone which are tied to the ex's account, means never being able to update them, which won't well for her.
I realize this isn't the simple solution you were seeking. But it is the best solution to let her start all over on her own Apple Account and be completely removed from the ex's account.