Really sorry for you, as I do for anyone who has been cheated on. But I must point out that your situation is a little sadder. You treat your wife like a queen and look at the reward you get in return.
Of course it's complete bullshit for her to say she doesn't feel like she's getting any attention to justify her cheating, but think about it, what can you do to avoid being cheated on? NOTHING.
When it's not enough for her to have the best husband possible, how can the atmosphere at home satisfy her when you reconcile?
Normally, I'm not much of a supporter for R, but I still express my opinions on what BSs who want to R should do. In your case, I can't even think about suggesting R.
Cheating is one hundred percent on cheater. But we might think that if there were things you could fix, it might have been harder for her to convince herself to cheat. But no, in your case we can't even say that. We can't say why she cheated or what it takes not to cheat again. And it seems that nothing could stop her from cheating. So how can you be sure it won't happen again in the future? Unfortunately you can't.
She wanted and did it. Hurting you, destroying your family, who the father of her baby is, etc. she didn't care at all.
I'm sure the idea that AP is the baby's father was also a good excitement for them. Moreover, I don't know if your newborn was there or not but that facetime call maybe meant to show her to her father(!). Happy that she is yours.
Let's get this clear, she's sorry for herself now, not for you or for destroying her family. She knew the risk she was taking, and it must have been worth it because she kept going until the end.
Don't feel obligated to do anything. You don't have to try for your daughters. It is better for them to have happy co-parents who love them rather than an growing in an unhappy family. The newborn will already perceive this as the usual order.
As for you, I'm sure you still love your wife deeply. But think, is she really who you think she is? A cheater and a liar, could you really love her? This is her reality. Maybe you also think of subjectively nice things about her and you say "that's not her".
What you think of the cheater when you hear about this happening to someone else, that's her. She showed you who she is, believe her. You were the one who made an effort for your marriage even when she was not in an A. She wasn't who made your marriage and your family beautiful. Actually, it seems that they weren't good enough for her anyway. She chose to give the love and attention she could give you to another man.
You don't love her so much because she deserved and earned your love. You love her so much because you can, that's the way you love, nothing to do with her. I'm sure you love your kids, your parents, your friends etc. the same way. Can you say that if you loved another woman you wouldn't do what you did for her? See that you're the prize, and she didn't appreciate it. She didn't deserve you and shouldn't have you.
I suggest you don't give her a gift she doesn't deserve. And you can't even be sure that it won't happen again. What is it worth if she swears a thousand times?