I am assuming you want to communicate between two apps. For that there are several ways.
To open other app within an app, please check this answer here.
Solution 1:
Don't use two apps to do single animation. Thats not good practice and not feasible. Do animation inside your iOS app and I believe iOS is powerful enough to handle your animation. Apple has already suite of game technologies to support gaming development in iOS natively. You can check this link here.
Solution 3:
If you can build app in unity, build whole app in unity.
Solution 2:
The first part of your question is very confusing though. You want to show animation in your iOS app but want to create animation in unity app? That is not going to work. Because when you open unity app, the current app will be suspended as default and you will only see unity app at that time.
As per your 2nd part of the question you want pass some arguments from iOS for animation to play in unity app. To do that you have to save data locally (in some kind of database whatever you like), like Number of total ball, Number of ball to ball generate, Ball colour code. And then you have to do code for unity to read those parameters from database and do the animation accordingly.