Yeah, it's not the best age to find out that one's parents are 1) sexual, and 2) unconventionally sexual.
That said, I do think that telling her there are more many ways to be married (maybe make an analogy to same sex marriage if that seems right to you) and many ways to be in a relationship. You've already started doing this and I would continue talking about those points. I would suggest emphasizing that all involved have explicitly consented and that everyone knows about everyone else. This will be good for her to know right now about her parents but I also think that consent and openness/honesty should be emphasized to all young teenagers. You should still be her role model in how to be in relationships.
I would also emphasize that this will not change her life - just her perception of her parents. You two are not divorcing, moving in with your other partners or anything like that. Her life will not change. And, as her life doesn't change and she sees that you and your spouse are really still the same in daily life, she will likely relax some. Or not. 13 year olds can be so hard core!
She may have lots of questions and not know how to ask. Or she might want to know inappropriate things, like what you 'do' with your other partners, etc. You and your spouse will have to think about how to handle her appropriate questions, encourage her to ask questions in general, and how to tell her gently to back off when/if she asks something too private. Talk about that now between the two of you.
You will also need to think about how you want her to tell, or not tell, other people. Some people that age are completely incapable of keeping a secret or being discreet in general. So you will have to figure out how to handle telling her what she can disclose and what is inappropriate for others. I would NOT treat it as a secret, never to be told to anyone, ever. That way it appears you are shamed by what you and your spouse are doing with your other partners. And no one can sniff out shame and hyprocrisy like young teenages. But she may well get the idea that what you two do, and with who, is your business, and no one else's, and so does not need to broadcast to all. Again, the gay analogy - no shame to be gay but the only person who can decide to come out of the closet is the person in the closet and that it is wrong to 'out' someone against their will - may be helpful.
Finally, have you dealt with the snooping issue? A very human thing to do but also totally unacceptable breach of your privacy, in my opinion.