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.
It appears that this child was born before the man signed the marriage contract with the woman, so this child is not his son. The female relatives of this man -like his sisters -have to wear Hijab in front of him.
If the woman was pregnant with this child from another man before she married this man, then it becomes clear that the child is not his son. However, is she was impregnated by this man [who is now married to her] before he signed the marriage contract with her, then the child is born out of an illegal sexual intercourse, and therefore, he could not be traced back to this man but should be traced to his mother, as the Prophet said: "The son is to the bed [should be traced back to the mother] but the adulteress will be stoned to death." [Al-Bukhari and Muslim]
This adulterer [this man] and the child can't inherit each other [as the latter is born out of an illegal sexual relationship] and there is no family relationship between them; rather, this child is a stranger to the adulterer and to the adulterer's family.
The mother of this child should abide by the Islamic rules and there is no need for problems with the family members of this man as they have the right to wear Hijab in front of this child and have the right to prevent him from entering upon them [without the presence of one of their Mahaarim (non-marriageable male relatives)]. Indeed, the Prophet said: "Beware of entering upon (marriageable) women." [Al-Bukhari and Muslim]
The Prophet further said: "No man should stay with a lady in seclusion except in the presence of a Mahram (unmarriageable relative)." [Al-Bukhari] The child is not a Mahram to them.
Finally, it should be noted that if this woman gave birth to a child from the second husband and the first child had suckled her breasts 5 times his fill, [before reaching the age of two years] then he is considered as a son to the second husband by suckling relationship, and thus, he becomes a Mahram to his female relatives.
Allaah Knows best.