I wish you the best in working things out. Since you've chosen to give your relationship a chance, there must be very solid reasons behind that decision - especially if there are children involved.
Many relationships have been strenghted by being tested in one manner or another.
It sounds as though you've considered all the facts, and are on your way to facing a new beginning. It is your decision now, so you can fully embarce it.
Don't forget to take care of your inner self along the way.