I believe you were on the right track when you first said F=ma because in the end Force plays a big part in deciding where the two objects will end up. So, this problem doesn't give you the mass of these children, but gives you their acceleration. So, the total mass of the children will need to be taken into consideration. What the teacher may be looking for is the amount of force is applied to the children, because it would decide where they would fall. Ex: If the force applied from the child on the left was 10N and the other was 5N then the child on the right would fall backwards 5N to the right. If they both were 10N then the netforce would be 0N, so therefore theoretically they would both just fall down in the same spot due to gravity. Hope this helps.
