In order for the movie to become as good as it can get, here are three pieces of advice:
1. Turn your phone in landscape i.e. on its side. This is to use all of the screen space.
2. Shoot in short bursts, i.e. try and capture the moments in 10-20 seconds clips or add movement and get one long clip that descripes what's going on.
3. Get coverage, this means step back, get a different perspective, a wide shot of the action or a reaction shot of mummy/daddy is great or close ups of the action to better explain the moment.
The above are not always possible but just a few more angles that just one shot will help your film tell a better story.