Ok sunshine. I think I understand your situation. Now it is that you are not married because of financial reasons. You would not be able to insure adequate medical attention for your daughter if you were to marry as your deceased husband's legacy allows you access to that insurance. I think I got that right. If not, clue me in. I would guess ex-military.
You also receive some sort of death benefit as a widow. And you need the funds to be able to be in effect a stay at home mom for her. Around here that is called SAHM.
In my comments, I am going to address your situation as if you were legally married. In fact, in many places you would be what could be called a common law marriage, something that was all many people had many years ago.

This site and associated forum follows Dr. Willard Harley's marriage plan and also his strategy for the reconstruction of a marriage that has been tainted by adultery. Your first task is to read his basic concepts, which you will find at the link at the top of the page or in right hand menu. Either one will work.
I do suggest that you find the book Surviving An Affair by Harley and read it as the best of the best for advice and direction. Most importantly, he outlines a plan for the restoration of a marriage. Buy it and read it, please. It is available at most book stores, especially those which sell Christian books, although it is not especially a Christian Publication.
The roles of people who post here fall into many categories. I like to get to know people and see what their heads are telling them. Others post very specific elements of Dr. Harley's advice and are quite good at translating that into effective guidance.
By all means if you have any questions about Dr. Harley's methods, this is the place to ask for opinions and get answers besides the Harley's themselves. For those who can afford it, I often recommend that folks use the Harley Coaching Center and pay the professionals there for help. They are very, very good at what they do, and even though they often charge a bit more than your usual therapists, they get more done in a few sessions than most therapists get done in dozens. They are really that good.
First at bat: Your guy MUST and I mean MUST, practice NO CONTACT with his affair partner for LIFE, period, end of story. Without that, nothing is possible, zero, nada, won't happen. This is a central deal for Harley's advice. And those who have been down this rocky road believe in what he says on this issue.
No Contract For Life, Period.
Now, please understand that there is great hope for those who get with the program and follow the path. If both you and your husband will follow the path, you can establish a marriage that will be a blessing for both of you. And don't worry if he won't sign on right away. Somebody has to lead and that will be you.
Now go read dear lady. And post your questions.
All the best.
Larry