Would you leave?

I'm just going to start by saying I'm a very, very forgiving person. Well, I'm too forgiving which is a serious downfall of mine. My partner has a history of being a dishonest person when it comes to his interactions with his co-workers and I have a history of just accepting it. I had forgot about an email he had made maybe 2 years ago and it was brought to my attention after he was charged 10 bucks for a membership he no longer has. I told him I'll fix it for him and thus came to light the email. He had sent out an email nearing the end of 2016 which is after we got our first home together. The email was sent with inappropriate intentions and he claims he had no clue who sent it. He claimed he forgot about the email despite signing on with his working phone and it was connected to his xbox account. Idk, I'm just tired of forgiving him and being ignorant as fuck. We have a 17 month old and another on the way and it terrifies me to be alone. I have no clue how to handle this on my own...I really don't have no place to go..or the finances because I'm on bed rest. A part of me says forgive and the other says don't be a fucking idiot