Welcome to the club that no one ever wanted to join.
I am going to lay a few things out for you, because you seem completely lost and overwhelmed, sleep deprived, and probably not thinking very clearly at this moment. If this comes out as harsh, it is only because you need to take control of this situation, and stop being a victim. You have to do that to care for your daughter who needs her Mom very much, and shouldn't have to be faced with Mommy being sick/sad.
1. Go to your Dr. Go now. Go to an emergency room, and free clinic anything where you can get medical care. Explain your situation that you spouse is having an A, and that you are completely overwhelmed by all of it, and that you have not slept in a month. Get some meds. You need to be able to sleep and eat. Also have some idea of how much weight you have lost. This is putting a huge strain on you physically, and if you don't stop it you will end up in the hospital, and that is not where you want to be.
2. After going to the Dr and getting some sleep, you need to go to a lawyer, and find out what your legal rights are in this situation. Your spouse has basically abandonded you. You don't want a D, I get that, no one does, but honey he has given you zero options here, other than living in misery, or filing. You don't have to file, but you do need to know what your rights are.
You will get some strength from this too.
3. Let your family know what is going on, allow them to help you, and support you. It's ok. No one gets through this shitstorm alone, and given your set of circumstances, and your strong physical reaction you need help right now.
4. Go to the store, and get some Ensure, or Special K protein shakes, Gatorade, or other sports drink. Part of your physical symptoms come from the fact that your body is not getting proper nutrition. This too keeps your brain from working right.
5. Get MAD. This Asshole, the guy that is supposed to be a great father, and spouse has sent you away because of 'financial' reasons, only to turn around and play the dating game with some other woman?!? Seriously, and now he has the audacity to tell you he loves you both? FTG he loves no one but himself, and only has his self intrests in mind. He wants to play the fun game of Dad, and Boyfriend, and Husband, but you are not going to allow that, YOU do not deserve this abuse, and it is abuse. YOU are a Queen, and your kingdom can survive just fine without a King, and certainly without a King that is really just a joker. DO NOT TRY TO NICE HIM BACK. THIS DOES NOT WORK. Ask any of us who have BTDT. You need to dig in your closet and find your Red Leather Stiletto, Silver Studded, Platform Bitch boots and put those suckers on and take control of this situation NOW. If you don't you are only allowing him to continue to hurt you.
Listen this sucks, it's painful as hell, but the winners in this game are the Betrayed Spouses that get their shit together, and start putting their and their childrens needs first. Your daughter does NOT need to think that this is normal, or what a marriage is all about. Get mad for her. You can do this. Oh and when that Bitch contacts you again, you best be ready to send her your own personal version of an No Contact Letter.
Please do these things for your daughter and yourself.