Using APIs like that is possible but really cumbersome and slow. Why canĀ“t you access data from your 1st app (parent) if your second app (child) is built on top of it? You should have access to all parent relations from the child.
If you need access to child relations from the parent (eg. the other way around), then you could redesign your relation structure so that the shared data is accessible to both apps inside the parent. This would save you a lot of work & headaches in the future. You can do that in existing apps by creating new structures, reimporting data into them and then deleting the old structures.
Going through APIs everytime your data access does not work because of a badly designed structure, will get expensive very fast as API exchange always has overhead and can get complicated when conflicts occur.
But to directly answer your question: You would need to call another API first by creating a record, which executes a backend function via trigger, which can do whatever you need. The filled relation can then be retrieved via a 2nd API. It is currently not possible to directly execute a backend function via API without executing a trigger in some fashion.