This was a simple but cute puzzle, and thanks again to Suman Saraf for suggesting this one. I received correct answers from Deepak Jayaraman (a first time participant), Pratik Poddar and Vishal Poddar. Well done all!
Here is the answer (copying directly from Deepak Jayaraman):
Question to Child 1 – Does either of the other two have two chocolates?
Yes – Child 1 has 2 Lollipops
No – Child 1 has 2 Chocolates
May be – Child 1 has one of each
L = Lollipop, C = Chocolate
If Child 1 has 2Ls then the other two have CC, CL – C1 can say with certainty that one of them has 2 Cs
If Child 1 has 2Cs then the other two have CL, LL – C1 can say with certainty that neither of them has 2Cs
If Child 1 has LC then other two could be CC, LL or CL, CL – C1 is not sure if either of them has 2 Chocolates because that is a 50% probability
Hope you all enjoyed the puzzle!