All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
This non-Muslim woman whom your husband married before, if she is from the people of the book and his marriage to her met the conditions of a correct marriage then that marriage was correct, and the children he had with her are considered his children. However, if she is not from the people of the book and does not believe and/or follow any religion, and he married her believing (due to ignorance) that his marriage to her was valid, then that marriage is null but the children will be traced to him as this is a controversial marriage. In both situations, the children are traced back to him. If it is religiously proven that these children are his, then there is no consideration to other claims, or to DNA testing. Saying that the children are not his is a very serious matter and is not confirmed except after proving this to be the case.
However, if he married her knowing that she did not believe in any religion, and he knew that it was forbidden for him to marry her then his marriage to her is void and his children are a result of an unlawful relationship and it is forbidden to trace them back to him. So it is not permissible for you to let this boy who reached the age of puberty [while your husband is not present] to be in seclusion with you or do anything else which the Mahaarim (plural of Mahram, a non-marriageable relative) are permitted to do.
Allaah Knows best.