| Okay! If the plys are coming apart, I would:
1)Get yourself two THIN, long spatula knives (no sharp edges). Gently insert the knife (dry) into the open ply-seam, and "feel" how big an area is actually loose. It might be bigger than you expect.
2)Take the knife out. Using one knife as a mini-lever, *lightly* work the ply open and insert the other knife (this one has glue on it) into the opening. It doesn't take much glue to do the job, so don't over do it. Operating the lever-knife will help spread the glue where it needs to go (capillary action.)
3)After your clamps are on, WIPE! Too many luthiers, professionals included, don't wipe. Excess glue is annoying, ugly, and rude. A damp paper towel works fine.
4)I would use yellow alphatic glue (Titebond or such). However, for this application, the glue should be lightly thinned with water. Not much, just a few drops so that the glue has a thin honey consistency. It's usually quite thick right out of the bottle. Squeeze some into a baby food jar, then add water. You can use hide glue if you want, but it's not neccesary for this particular task. Yellow glue has a FEW uses in the shop, and this is one of them.
BTW, do you have clamps for the job? | 
