My wife is three years younger than I am. She worked for 12 years. My FRA social security benefit will be over 2x hers. I plan to file for retirement at 66, my FRA. My wife plans to file for her benefits at 62 and then when she reaches FRA at 66 1/2 she will file for spousal benefits. Will her survivor benefit be decreased because she filed for her own benefits at 62?
No, the reduction that your wife would take to start drawing her own benefits at age 62 would not carry over to her benefit rate as a widow. If you die after she reaches full retirement age, she would essentially receive the higher of your benefit rate or her own, even if she took reduced retirement and/or spousal benefits.
By the way, assuming that your wife was born after January 1 1954, whenever she files for benefits she will be deemed to be filing for both retirement benefits on her own record and for spousal benefits (https://www.ssa.gov/planners/retire/deemedfaq.html). She can't take reduced benefits on her own record at age 62 and then switch to an unreduced spousal benefit at age 66 & 1/2 as you suggest in your question. However, if you haven't yet filed for your benefits when she applies, she won't be eligible for spousal benefits until you start drawing your benefits.
You may want to strongly consider running the maximization software available on this website in order to determine the best filing strategy for you and your wife.