Is there a way to have one apple id for the app store and another apple id for apple music?

No. The Apple ID used for the Store is the same one that is used for Apple Music.

You can use Family sharing from the Apple ID that has the Apple Music subscription to share it to the other Apple ID.

click here ➜ Share Apple and App Store subscriptions with family members on iPhone - Apple Support

Subscriptions are tied to the Apple ID used to start them in. If you change the Apple ID for the App Store the app subscription will no longer be available on the device, but will continue to charge the payment method on the Apple ID you used to start it.

The Apple ID used to start the Apple Music subscription will be charged for it and will use whatever payment method is tied to it.

Your best option to keep access to the App subscription and be able to access Apple Music at the same time is to use Family sharing to share the Apple Music subscription.