Well, you can't reuse the sinew. There's really no way that I can imagine to reconstitute it.
My feeling is that if you do find a way to glue your sinew flap down, the bow back likely won't have the entegrity it should have with multi-layers of sinew. Part of applying multiple layers of sinew is to create random, interlocking locations of the seams. If I am visualizing your tear correctly, by laying it back down and glueing it, you will have 3 layers of sinew in a location all with the same seam. It will always be a vulnerable spot. That Hupa style, short bow is put under a tremendous amount of tension and even if you wrap around the limbs I predict the repair will again separate at the 3-layered seam. I agree that transverse wrapping during the initial construction of the bow is likely necessary, especially with 5 layers of sinew. I don't feel that it will provide a failsafe remedy to the already compromised 3 layer tear.
As far as removing all of the sinew and starting over with the sinew process, I would hesitate to use the same wooden core. If the 3 layers of sinew tore, I would think that the core wood suffered some damage, as well. Rather than putting more time and material into this bow, I think that I would consider it a learning experience and start over. Like the others mentioned, a picture would be interesting to see. A picture might help identify what went wrong. Afterall, you could use a combination of all of the advice in this thread but if you don't identify the original cause of the failure, if not corrected you may be in the same danger on your next attempt.