This is where I fear I may lose @RocketRaccoon...
Excuse the language. I mean it all very gently and lovingly. Please bare with me.
So clearly, you've turned your daughter's world completely upside down. Is it your fault? Yes. Your shitty decisions are what led you where you are today. Lies, deception, betrayal, lack of boundaries, and the list continues. So...where does it stop?
Do you love yourself? Do you see your own worth? Can a mother who doesn't love herself effectively navigate the kind of painstakingly unconditional love that their child deserves? If you can't enforce your own boundaries, then how can you help set boundaries for her?
You know what shitty looks like. You've defined that part. I think, no, I fully believe...you also know what better looks like. Dig deep. You, at the very core of your being, would never (under any other circumstances) allow yourself to act the way you are acting now. I don't mean the affair. That's done. It can't be undone. I mean the weak, pitiful, woe is me LD that we have all seen since you had to admit your failure to the world.
You made shitty choices, I get it. I've been there. Now is the time for you to start making the right ones. The ones that solidify you're a stronger woman than one who will allow her past to define her.
Tell me...
30 years from now your daughter comes to you and tells you that she did exactly what you have done to her own BH. What advice do you give her? Would you choose for her what you are currently choosing for yourself?
Would you tell her: "Look mini LD, you done fucked up...now you must pay your penance." You must choose to present yourself as a broken doormat, at the expense of your own child. This is the only way you can redeem yourself.
You displayed shitty boundaries. Your BH saw that. Now, his request is that you display them again in the name of his healing. (Everyone please bare with me before you get out the pitchforks).
The pain you inflicted on him is immeasurable. He doesn't know how to process it. He's trying. He's doing his best. He can't figure out if/how to move forward, so he's decided not having to look at you is what he needs right now. You've accepted his words about his current needs. Limbo. Separated limbo. It's a bitch. The problem with limbo in your situation, is that you're both so focused on the pain LD caused, that you've both failed to realize there is a beautiful 5 year old who is in limbo right with each of you. Limbo is damn near psychologically impossible for adults to deal with. How should she be expected to manage?
My opinion, as unpopular as it will probably be, is that if he didn't still love you...he would have already divorced your ass. Is love enough? Maybe. Maybe not. At this point, does it even matter?
When two people make the choice to bring another human into this world, they take on the responsibility of giving that little human everything they have to offer. Take the vow "in sickness and in health," and add "because how you model your life will forever shape theirs."
Work together. Teach her that adults are flawed. Teach her the meaning of forgiveness. Teach her the importance of honesty. Teach her that every action has a reaction. Teach her redemption. Teach her you don't have to be a prisoner of your past. Teach her how to do better. Teach her how to be better than both of you. Teach her self love. Teach her confidence.
Talk to her father. Tell him your needs. You know...the ones you're so desperately afraid he will reject because of your betrayal. Teach her that no matter how much you want something, if you're afraid to try, the answer will ALWAYS be no. Teach her to never fear advocating for herself, and if the answer ends up being no...how to walk away with her dignity still intact.
Once you decide to stop being frozen in fear (ironically because not too long ago your bs was frozen in fear too), then you can feel confident in how to actually move forward.
I get the feeling, as unpopular as it may be, that both you and your BH are allowing outside influences to trump your actual needs to heal.
If you need to heal together, then you need to band together and show her how it's done. If you can't heal together, then you still need to band TOGETHER (as far as she is concerned), and show her how it's done.
If you two can't give her (while together) the solid foundation she needs, then you two still need to (as a united front) give her the solid foundation she needs.
Essentially, figure out how to be lovers again, or figure out how to love each other in the sense that you share a single most important common goal. Her. You can't do that from a separated limbo. You both may think it's your own relationship that's in limbo, but really it's her that ends up there.