Hi Larry, et al. --
I was married to my husband 9.5 years, then divorced, and then he died. I have three children (now aged 11, 11, and 7), who are receiving his survivor's benefits. Would I still be able to claim divorced widow benefits, without compromising their benefits (or at all, since we weren't married 10 years)?
Assuming that you're unmarried and have at least one of the children in your care, you can file for surviving divorced mother's benefits, but not without potentially compromising the amount that your children receive. That's because that, although there is no marriage duration requirement for surviving divorced mother's benefits, they are subject to the maximum family benefit. Furthermore, there is an earnings test (https://www.ssa.gov/planners/retire/whileworking2.html) that could limit payments to you if you are working.
If there are 3 children currently receiving benefits, their individual monthly rates are almost certainly already being reduced due to the family maximum benefit payable on your ex-husband's record. So, if you file now, the likely result will be that the family maximum will be split 4 ways instead of 3. In other words, the total amount payable would remain the same.
You may want to double check with Social Security to make sure that the family maximum benefit is already being paid to the children. Also, if one or more of the children becomes ineligible for benefits in the future (e.g. turns 18 and isn't in high school or disabled), and if you still have a child in care who is under age 16 or disabled at that time, it might be advantageous for you to file then if you haven't already filed.