As far as I understand Yes, that is correct. As far as the couple needing to remarry according to Halacha. They will separate, and re do the whole process, and mikveh and everything.
But your reference to mamzeirim I think is incorrect. This is NOT an issue of mamzeirim at all. To my knowledge (which is very limited) I think a mamzer is only is a woman had a child of another man while she was halachically married.