Answer
(Fatwa: 2705/H=1093/th=1431)
(1) Islam accepted merely to marry a Muslim man is generally not deep rooted. Hence, a Muslim man should take such step after due consideration. However, the detail about the validity and invalidity of the nikah mentioned in the question is that if that woman married immediately after accepting Islam while yet three menstruating periods were not passed, then this nikah was not valid and the child too will not be considered legitimate.
فى رد المحتار: لو اسلم أحد المجوسيين ثمۃ ای فی دار الحرب ۔۔۔ لم تبن حتی تحیض ثلاثا او تمضی ثلاثۃ اشھر قبل اسلام الآخر (شامی 4:363)
But if she married after passing three menstruating periods, then according to one opinion, the nikah will be valid and the child too shall be considered legitimate. Though still it was better for her to marry after passing three more menstruating periods.
(2) It is haram and unlawful to ignore the first wife and children and marry a non-Muslim woman in un-Islamic way. It is open injustice on previous wife. Thus, it is wajib on this person (your husband) to do tauba immediately and remarry that woman Islamically, and do complete justice between both the wives and pay the rights of the children. Hadith warns sternly against it.
Allah (Subhana Wa Ta’ala) knows Best
Darul Ifta,
Darul Uloom Deoband