My kids lost their father in 2012. They each received approximately $333 per month till my oldest turned 18. The remaining two each received approx $575.the second child turned 18 and my youngest whom is 16 only receives $575. I did not receive any benefits due to being divorced and only married for 7 years. Why is the 16 year old only receiving $575?
The amount that your 16 year old is receiving is apparently 75% of their father's primary insurance amount (PIA). That is the maximum amount that a surviving child can be paid, but there is a family maximum benefit (FMB) on each worker's record that sometimes limits the amount that each child can be paid to less than their full rate when multiple children are eligible for benefits on the same record.
For example, say Vic is deceased and his PIA was $800. The FMB that can be paid on Vic's record is $1200, or 150% of his PIA. If only 2 children are eligible for benefits on Vic's record they can both be paid their full rate of 75% of Vic's PIA, or $600 each, without exceeding the FMB. However, if 3 children are eligible for benefits on Vic's record they would have to share the FMB and each receive $400.
Regarding your eligibility, if you haven't remarried after your divorce then you likely would have qualified for surviving divorced mother's benefits (https://www.ssa.gov/OP_Home/handbook/handbook.04/handbook-0416.html). Surviving divorced mother's benefits are also paid at a rate of 75% of the worker's PIA, but are subject to the FMB. There's no duration of marriage requirement for surviving divorced mother's benefit eligibility, but you must have a child of the worker in care who is either under age 16 or disabled. However, it sounds like the FMB on your ex's record was already being paid while there was at least 2 eligible children, so if you had filed for benefits when 2 or more of your children were drawing benefits then any benefits that you received would likely have reduced your children's benefits by an equal amount.
Now that only one of your children is drawing benefits, if you were still eligible for surviving divorced mother's benefits then you could be paid those benefits without reducing your child's benefit rate. But, unless your 16 year old child is disabled you would no longer meet the requirements for surviving divorced mother's benefits. You could claim those benefits for a maximum of 6 months retroactively, though, so you may still want to look into applying for benefits if your youngest child turned age 16 within the last 5 months or if he or she is disabled.