Hello! When making oreo suckers I've encountered some frustration with how easy the cookie breaks when inserting the stick into the filling. Sometimes, the cookie part will even seperate from the filling! Not good. After some experimenting, I have found some tips that helps minimize these problems:
Gently twist one of the cookie parts away from the filling; using the candy stick, scoop some of the filling away.
Lay the stick where you scooped the filling away and smooth some of the filling back over it.
Very gently, twist the cookie part back on.
Sometimes, it will still break. As long as you can keep the two pieces together and press it back into the filling, it should still work. Just be gentle when you're dipping it in the melted chocolate.
Also, as an extra tip, I used a regular mug to melt the melting chocolates in--the deepness of the mug allows better coverage of the oreo while dipping.
I hope that helps! Have fun!