Hi Mayhs,
I face a similar dilemma, being an MBA myself and aspiring to do another one. After having researched a lot of websites and the applicant pool for many global b-schools, I have come to a conclusion that names of the degree per se will not be able to fool the adcom folks, they are too smart to understand the content of the course.
Does that mean that we do not have any option; no not really. There are lot of b-schools like Harvard, Wharton, IMD, IIM-A, INSEAD etc where Indian students who have already done an MBA have gone ahead to do another one. The recongnition of Indian MBA abroad (to understand that a PGDM/PGDBM/PGDCM etc is akin to an MBA) is fairly ok. I think , you can do two things:
1. Try to find out more about schools where a second MBA is a clear no-no. Apart from what is mentioned on the website , I have heard that Tuck clearly discourages this, there are a few other american b-schools where this is an entry restriction. Once you can generate a rough list of such schools, you can cancel them out from your pool and focus efforts on the remaining ones.
2. For others also, an important part still remains justification of a second MBA. Even though you will know the reason yourself but it will have to be carefully and convicingly told.
I would be happy to team up with you on such searches, defining rationale etc.
BTW my degree's name is unfortunately MBA itself; so slightly more difficult case than yours


Regards,
Shravan