I think considering the ages of the children, their opinion of you will be the deciding factor in who gets to be their new nanny. So it is best if you try to win them over big time on your trial day.
The parents will be watching you as well so here are my tips:
1). Arrive five minutes early. No earlier than that. And not one minute past your due time. Really.
2). Show up with a huge smile on your face, a sunny disposition and your sleeves rolled up, ready to have fun and play.
3). Make sure you are knowledgeable regarding age-appropriate activities for the kids. Nothing too juvenile or mature for them. Trust me on this, the parents will take note.
4). Engage the children fully, yet not so much that it appears like you are trying to hard to impress. Be natural and do not come on too strong to the kids. Proceed in an organic fashion. See how the kids react to you, then respond appropriately. Do not be a phony.
5). Have your cell phone turned off prior to even entering their home. Don't even put it on vibrate. The best idea would be to leave it in your car the whole time. This will show the family that the children are your top priority at all times.
6). Be active, creative and confident. Keep telling yourself that you are the best nanny out there and they will think so too.
Good luck OP! Please let us know when you get the job.