how to get an app without parent permission on ipad through the children's account

If Ask To Buy is set up it needs to be approved. if you are an approver you can do it in person on the child's device, or on your device.

From: Approve what kids buy with Ask to Buy - Apple Support

See the section below for how to get approval in person.

How children or teens can make a request with Ask to Buy

1. To buy or download an item, tap the price or Get button. Or if you're using an Apple Watch, double-click the side button, then enter your passcode.

2. If asked, enter your Apple ID and password.

3. Tap Ask. If your parent or guardian is nearby, you can tap "approve it in person" and they can approve the purchase directly from your device.

4. After your parent or guardian buys the item, it downloads to your device automatically.