Does that make her children from the second marriage mamzeirim after Techias HaMeisim since her original marriage is still valid?
The Wolf
Since the marriage is not an illicit relationship, they are not Mamzerim. The case of Ba’a Memedinas Hayam they are Mamzerim, because even though she is allowed to marry, sof davar, the relationship is illicit (i.e., we only allowed her to marry due to our own ignorance, not due to it actually being muttar).
Think of it like the Torah allowing the woman to marry a second husband. The child would not be a Mamzer in that case.
As far as the Ben Ish Chai, the death of Klal Yisroel was permanent, and required an Act of God to reverse. As far as Keddushin is concerned, the point is good but questionable. BB 120a talks about Amram doing a “Maaseh Lekuchin” to Yocheved to take her back. Also see Rambam Ishus 1:1, and a similar question exists there.
G@W