The effective date has nothing to do with your dad's passing. You state that you filed in 12/10, and the effective date would be based on the date of your application for your mom.
Actually the effective date of the award is the first of the month after the veteran's death assuming that the application is received within one year from the date of death. The effective date of the entitlement is the first of the month of the veteran's death. There is an odd and difficult to explain distinction in the law.
Please also note that the application you submitted (VA Form 21-534) is actually an application for DIC, Death Pension, and Accrued benefits. While she may have only
wanted to apply for death pension, the application is for all three benefits, so VA must make sure to address all three of them.
Please let me know if you have any further questions.
The $132.00 represents what her monthly entitlement is starting December 1, 2011. This was because her expenses decreased. My guess is that she reported funeral expenses of a few thousand dollars. The funeral expenses can only be considered for one year, so the award decreases to account for that. My guess is that they did not consider all of her expenses because they were either not completely reported or the information included with them was unclear. It is to her advantage for you to report her expenses quickly to account secure her an increase.