I am not sure where everyones info is coming from but the husband need not take permission of any sort from the first wife, nor does she have to sign any papers. She also has no legal recourse should he remarry. If the marriage is done in Sharia fashion both marriages are valid in states that recognize Islamic polygamy.

Now, the implications of a second wife are something all together different and life can indeed be miserable for all involved if the first wife doesn't know about the second and so forth and so on.