Please help! Husband wrote emotional love message to friend (ex) and I found it. He claims he faked it for "attention" to see if he 'still had it' but I'm not sure if I believe him. Need perspective. Possible divorce...? Love message (and her response) below.

Crosspost from r/relationship_advice
Backstory: Together 5 years, married for one. Previously I was working and he stayed home with our first child. With the pregnancy of our second child it was too stressful on me so I stayed home and he went back to work. He's gone Monday through Friday for work.
When we met several of his friends added me on Facebook, cool nbd. Recently I had an alert that it was one of his female friend's birthday. I've met her before, we chatted briefly, she seemed ok. I clicked and went to her page to wish her a happy birthday when I noticed our 'friends in common' no longer listed my husband. Now my husband is very sentimental and has had some friends since grade school- 10, 15, 20 years. He's also from a small town where it's common for everyone to remain friends (most often). He's a very likable guy and has over 1000 friends on Facebook from over the years. For some reason her missing from his friends list sent up red flags since I knew they had been close friends for years, wishing 'happy birthdays' and 'congrats on X' posts back and forth for years, and had briefly dated years before we met. That's when I decided to look through his messages....I honestly still regret it and do feel like an ass, but now I'm trying to figure out if this might actually save me more years of heartbreak. (I know that going through his phone is awful and I feel gross...when I brought this up to him the first thing I did was apologize. I've never felt the need to before now.)
What I found was a message from her, which seemed to reply to a message from him, but there was no recent message from him that matched. (Spoiler- He had deleted it.)
I went to his notepad app and found the long first message to her. These were sent 1 month before our second child was born, who is now 3 months old. The letter went something like this:: 'My heart is beating fast and I have wanted to tell you for a long time. You are the first thing I think of in the morning, and I dream of you at night. I love you, and only I can love you this way. We could have the romance story of the century. After all these years I've never stopped loving you. I dream of running away with you... living anywhere as long as I'm with you. there's only one woman that I love and that is you, YOU, only you. (He goes on and on romantically writing for many paragraphs, then ending with) all of this is not a lie because there would be no reason."
Her response was basically:: 'thanks for this, it made me cry reading it. I've never had a man write anything like this for me before. I had fun years ago (writes a little more about fun times) but unfortunately so much time has passed I don't feel the same way (then she reminds him of his wife [me] and children).
I confronted him the same day. I first admitted to going through the phone, then apologized. I told him what I found. He said he was going through a hard time with working and having a second baby, he said he felt like running away from himself and his responsibilities. He said he mentally ran away for a while. He said things got difficult and he had a weak moment. He said he spent a couple days writing that message before he sent it. He said he doesn't love her and that it was faked to try and get approval/attention and feel like he 'still had it.' He said he regretted send it. He said he loves me. He said he wants to grow old together.
The problem is that I know he never meant for me to read it. I feel like it's an inside glimpse of how he really feels. (Which is another reason I still feel ashamed for looking).
I'm so confused. If he can write like this and NOT mean it (as he claims) then should I believe anything he says to me? If things get tough again what will he do? If he can fool everyone into thinking he's the best husband (even me) while sending poetic love messages to another woman...who is he lying to: me, her, or himself? Does he really love this woman but just can't admit it? If she means nothing does he just miss that feeling of infatuation so he'll be looking for it again in the future, no matter who the person is? If someone doesn't reject his advances in the future what might happen? Do people write messages like this over several days if they really feel nothing? Could it be a one time **** up because of stress? What the actual ****?! How can I trust him?
While I feel like a divorce will be difficult, I'm not going to stay in a situation where my spouse is emotionally cheating and is truly in love with someone else. The kids are my #1 so I plan to be very amicable and insist we share custody for their sake. They love their daddy and this doesn't change that. Can this be fixed? Am I overreacting?
I feel like my heart is broken and I've been crying for days. Help me Dating.mobi...what are your thoughts?
Edit: tl;dr: Husband sent poetic love message to a friend (ex) he briefly dated years ago. I found it. He said he wrote it over several days, yet he made it up for attention because he was stressed about 2nd baby. Is that possible? Should I leave?


Source.

Oh hell no!!! He is saying he faked it cause he got dumped on. That letter was real! Get out and get out now.