Sorry,but as far as I know,there are no shampoos that "strip" hair of perms.The only thing to do is let it grow out...I somehow dont think you'd need to let it grow all the way out,most perms/relaxers last about 2-3 months depending on the hair. My advice is to ask other salons what they think as well to get a second opinion. Relaxers are extremely harsh to hair though,so they were right about the possible breaking off. You should highly condition your hair in the meantime,using hot oil treatments. Also,a great product is Nexxus emergencee~it really helps dry hair. When I straightened my hair (but to get a perm out,my hair is naturally straight) I used a home perm kit and brushed my hair straight (instead of using curlers) to straighten my hair. I have never heard of a Permenant hair straightening thing...it could be simular?
Anyways,it never hurts to get more then one salons opinon,but if they say it's a bad idea,it probably is....Godd luck!