Foreign court decree of divorce or dissolution of marriage can be valid in India provided such decree is according to the provision of law in India as provided under section 13 of the Civil Procedure Code and Principle of law as laid down by the Indian courts. A foreign court divorce decree may be valid in India ONLY if the spouse had lived in that country and had consented to that country's jurisdiction.
A foreign judgment shall be conclusive as to any matter thereby directly adjudicated upon between the same parties or between parties under whom they or any of them claim litigating under the same title except-
(a) where it has not been pronounced by a Court of competent jurisdiction;
(b) where it has not been given on the merits of the case;
(c) where it appears on the face of the proceedings to be founded on an incorrect view of international law or a refusal to recognise the law of India in cases in which such law is applicable;
(d) where the proceedings in which the judgment was obtained are opposed to natural justice;
(e) where it has been obtained by fraud;
(f) where it sustains a claim founded on a breach of any law in force in India.
So these six conditions are fulfilled by such foreign judgment/decree of divorce then it will be valid for dissolving such Indian marriage as has been held by the Supreme Court of India in several of its judgments.
In your case your wife has accepted the authority of US court, it cannot be open to her to later question the authority of the US court.1. If someone has accepted the authority of a court, it cannot be open to the person to later question the authority of the court. So her new case will not stand.
As per Indian law wife has no right over husbands self acquired property.But she can claim right to stay there .
Find a local lawyer and file your objections properly.