You will need to petition the court to determine paternity.
Since you were married to this man at the children's birth, he is the presumed father, however, the courts can change this with a DNA test done and ordered by them. You will need to go through the court to get another DNA test done. Once done, the court will then order that the father be changed on the birth certificates to reflect the real father.
At that time and once the paternity is ordered changed, you can also petition for a name change of your children to reflect that of the original father.
Having the other son adopted, however, is a trickier matter. To have the son adopted that is not biologically the mans you are with at this time, you would have to have consent from your ex husband to do so. If he refused, you would have to battle it out in court; however, it is very unlikely that the courts will allow his adoption if the man you are with is not the biological father and the biological father refuses.
I would highly recommend getting an attorney to help you in this as changing paternity and trying for adoption can be very complicated.
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