If I may I would like to clarify some.
Lorraine,
Is the divider that is sticking out a solid piece of wood that goes the entire length, or is it just a short stub tied to a web frame or a short stub on its own?
Is the top a solid piece of wood (I am guessing yes)
For your web frames, did you glue the the entire length in the carcass of the cabinet?
FWIW, the brads aren't a big deal in my opinion. They will bend when the wood shrinks and contracts. To me, it looks like your top has shrunk, but your divider has stayed in place, but it is hard to tell, and it depends on your construction methods.
Will it come back out in the summer? I would guess yes, but it will happen again, and IMO, it will weaken or get loose if you do not address it. Remember a large top will move maybe a 1/2" from summer to winter.
Clarifying one point that David suggested, you can screw the first 2" and not worry about it, but the remainder has to has screw holes widened to allow the wood to expand. Do not glue it past the first two inches. Brads would work as they will bend.
It seems to me your top and sides have shrunk while your frame has stayed in place. If you do screw the front two inches from the inside with pocket holes and screws as Alan suggests (which I have done to fix this type of issue and it does work) does the wood have the ability to move at the rear of the cabinet or is the back going to keep it from moving?
Lots of options and lots to think about. It does suck though. I learned the hardway with a headboard I built with raised panels. I made the panels too tight and that summer, it busted the joints apart.