Re: Idk what's going on.
Knowing that she had an affair and left you while married for someone else, how do you truly know where her truth lies? Do you think she is manipulating the situation and if so, are you walking into another round with eyes wide open understanding everything that has happened with not just you but her also, or eyes completely shut willing for anything including she could cheat on you again just to try to have a chance for your family to be together?
I feel if you are willing to put the past aside and place all your chips in the center of the table, so should she.
Let her know that you are not willing to accept being lied to and cheated on again, and that putting your family first means that honesty and transparency in everything must come and if that fails, love will not survive it again. You cannot control the outcome, but without both of you trusting the process of rejoining life as a family together and the work involved, her chance of failing you again will happen.
To go into this without conditions and standards is madness, she has to know up front that if she waivers again in her loyalty to your relationship that you will end the only opportunity she has to make the past mistakes right and you will end it with the confidence you did your best moving on with your life as the best dad you can be for your girls and whatever comes to her simply comes. She must have no doubt that any future outcome cheating on you again will end very, very badly as your family will be forever broken up.
You do not need to remarry to build a good family home, what you do need is trust and respect, love and kindness, giving and commitment, dedication and loyalty... if you can maintain this again for a longer time than when she ran out on you with another man while you were married, then think about remarriage, by then your foundation will be sound.
If your heart tells you this is right and your mind tells you it is worth the risk, take the step... give your children a hug as you do, I hear in your words they are worth this effort.