One of the tenets of DBing is "no R talk", but I think you need to make an exception and sit down with her.
I think you need to tell her that you're sorry, but you don't consider "keeping your wedding vows for 5 weeks" to be worthy of some sort of marital merit badge.
I think you need to tell her that YOU don't appreciate being cheated on, and then lied to, and then made to feel like YOU'RE the bad guy when you want to sleep in your own bed.
Tell her you love her (another supposed "no-no" of DBing, but I think you should reassure her here), that you DON'T want a divorce, that you DO want to work on your marriage, but only if it's with a healthy balance of each other's emotional needs.
I do think you need to validate how she feels about the sex -- that is very important to a woman, emotionally, and she probably does feel "used" in that regard (not saying it's right, but only that's how SHE perceives it).
But you ALSO need to tell her that MAKE NO MISTAKE, you will NOT tolerate her bringing the children into this, and saying the things that she's said to them about you "making her penniless," etc. That's is ABUSE, and that when it comes to your kids, you will do what is necessary to remove them from such a toxic environment, and is that clear???" (and I mean really LOOK HER IN THE EYES when you say this part)
I would tell her that it absolutely BREAKS YOUR HEART to hear her crying, and to see her in pain, but that you don't think it's good FOR EITHER ONE OF YOU for you to rescue her from pain that she self-inflicted "by deciding to have an affair."
Then I would hold her, I would kiss her squarely on the forehead, and say "let's talk more about this later," and then leave the room.
