I would definitely talk to each daughter (age 9 & age 12) separately, not together at the dinner table. (Or introduce the idea at dinner, then make separate conversations later).
There is a big difference between what you know/think about sex & relationships at age 9 versus age 12. Each daughter will probably have a totally different reaction.
Just as an example:
When I was 9: I had a crush on a boy who always asked for my help with his math homework. But when my mother told me that his mother told her that he liked me and wanted to dance with me at the ballroom dance lessons we were being forced by our mothers to take, I was so mortified I tried to get out of the dance lessons. At the dance class, I tried hard not to look at him or speak to him. Definitely I did not dance with him. I was terrified that he might want to kiss me, which would be disgusting.
At age 9, I was also trying to wrap my mind around the concept that a penis goes into a vagina and that this bizarre event creates a baby. Around this time, I learned about the concept of birth control & condoms, which confused me even more.
I remember being so perplexed that I was almost in tears, and I asked my mother: "If sex is for having babies, why on earth would anyone have sex with birth control? What would be the point?" My mother tried to keep a straight face while she explained that people have sex because it is fun. I was astonished, but also felt like a lot of things about the world suddenly made more sense.
I was convinced, however, that my parents no longer had sex because, my gosh, they were so old. I was flabbergasted to learn that they did indeed still have sex (with each other); so that was astounding enough without having to wrap my mind around a poly arrangement.
When I was 12: I desperately, desperately wanted a boy to kiss me. But I was convinced that I was so ugly no one would ever want me. I liked a boy who liked the popular, flirty, stupid girls that I hated.
And I had started thinking about sex constantly. I checked out books at the library only after browsing through them to see if they might have sex scenes. (I read way above my age level). I started sneaking romance novels into my room. I was very close to figuring how to give myself an orgasm.
By age 12, I also understood that my parents still had sex (with each other!), which was gross, but I did think it was nice that they were healthy and happy and that sex was a good thing in general.
I still had a LOT of questions about sex, but they were not at all the same questions I had had when I was 9.
1) a 9-year-old is still trying to figure out what sex is and why anyone would want to date anyone at all
2) a 12-year-old is trying to make sense of her own sexual feelings and is dealing with the horrible insecurities of adolescence
3) both kids will be more preoccupied with their own love lives than with yours!
So, please speak to them individually. (They will probably compare notes with each other later, in private, which is fine).
And I agree with the advice that your 12-year-old is probably worried that you are having an affair that will lead to divorce.
Single, straight, female, solo, non-monogamous.