A single judge from Nagpur bench of Bombay High Court held as follows,

From Para 9,

9. In order to appreciate the rival submissions, I have gone through the record and proceedings. I have also gone through the judgments relied upon by both the parties. It is true that as per Section 1 of the D.V. Act, the D.V. Act extends to the whole of India except the State of Jammu and Kashmir. It does not extend beyond the limits of India. The question therefore, is whether for the domestic violence caused to the aggrieved person on the foreign soil can be taken cognizance of by the Court of Magistrate in India at any of the places provided in clause (a) to (c) of Section 27. It is to be noted that subsection 1 and Section 27 of the D.V. Act will have to be harmoniously construed. The D.V. Act is a social beneficial legislation. The object and intention of the legislature behind this enactment is writ large from the statement of the object and reasons of the Act. Section 27 of the Act provides for the jurisdiction of a Court of Magistrate of First Class or Metropolitan Magistrate to entertain the application under this Act. The provisions of Section 27(1) (a) and (b) are applicable irrespective of the place of cause of action. It is to be noted that clause (a) and (b) of Section 27 (1) of the D.V. Act has, therefore, no direct nexus or co-relation with the place where the domestic violence was actually caused. In my view, these two clauses namely (a) and (b) of sub section (1) of Section 27 have to be harmoniously construed with sub section 1 of Section 27 of the Act. If it is so done then it would show that the law makers were mindful of such a situation and therefore, Section 27 have been worded in this form. It therefore goes without saying that though the Domestic Violence Act extend to the whole of India as provided under Section 1 of the D.V. Act, the domestic violence caused on the foreign soil could also be taken cognizance by invoking Section 27 (1) (a) and (b).

From Para 13, (Dumb interpretation)

13. The Hon’ble Apex Court has observed that sufferings of the wife at parental home though may not be directly attributable to commission of acts of cruelty by the husband at matrimonial home but the same would undoubtedly be the consequences of the acts committed at the matrimonial home. It is observed that such consequences, by itself, would amount to distinct offences committed at parental home where she has taken shelter. It is further observed that adverse effects on the mental health in the parental home though on account of acts committed in the matrimonial home would amount to commission of cruelty.

Not sure, which of the 6 reliefs, if/when passed by Magistrate Courts in India, will be executed outside India and how?

Index of DV Judgments is here.