The guiding principles for Courts(Both international and indian) to grant divorce petitions are :
(a) the lex loci celebrationis (ie, the law of the land where the marriage was celebrated);
(b) the lex fori (ie, the law of the forum); or
(c) the lex domicilii (ie, the law of the domicile).
Since your marriage happened in India under Hindu Marriage Act and both of you being indian citizens, Indian courts alone have the jurisdiction to grant divorce.
Please pursue the judgment of Singapore High Court in Sanjeev Sharma s/o Shri Sarvjeet Sharma v Surbhi Ahuja d/o Sh Virendra Kumar Ahuja,  SGHC 104, Suit No: Divorce Suit No 1698 of 2013 (Summons No 7877 of 2013), (Registrar’s Appeal from the State Courts No 6 of 2014) . This judgment should give you enough insights on how singapore courts approach divorce under Hindu Marriage act.. This judgment also talks about the Supreme court of India's judgments on divorce decrees's by courts overseas under Hindu Marriage act.
The key rule laid by the Supreme Court on foreign divorce decrees can be summed up as follows: If a couple is
married under Hindu law,
(a) the foreign court that grants divorce must be acceptable under Hindu law; and
(b) the foreign court should grant divorce only on the grounds which are permissible under Hindu Law. The two conditions make it almost impossible for a Hindu couple married in India to get a legally valid divorce
from a foreign court since no foreign court is an acceptable one under Hindu Marriage Act and also because no foreign court is likely to consider the provisions of Hindu Marriage Act before granting divorce.
Now coming to review of your plan of action
a) You (not your sister through POA) should file a petition for Restitution of Conjugal RIghts under Sec 9 of Hindu marriage act in the family court in andhra pradesh. A restitution of conjugal rights petition can be filed only by the husband or wife and not through POA or lawyers.
b) Once a restitution of conjugal rights petition is filed and your wife files a divorce petition later in andhra pradesh, you can approach the high court of andhra pradesh for staying / transferring the case to one court (either at Wife's place or at Husband's place) depending on merits.
c) The family courts in India or for that matter any court in India cannot stay the divorce petition filed in singapore(refer the Judgment of The Madurai Bench of Madras High Court , dated 18/09/2009, in CRP(PD)No.525 of 2009, between Bharathi VS Mahesh Kannan
d) SIngapore courts are not duty bound to recognize the orders of the courts in India. So it is better to inform the singapore court that the petition has been submitted in indian courts for restitution of conjugal rights in india and not expect any thing more from it.
e) Child custody - better that children are with either your parents or your wife's grand parents, till you both decide on child custody in courts.
So overall given the above facts and issues, i think you have the right strategy in filing a RCR in india and if at all the proceedings lead to divorce, then better proceed with the divorce case in india.
Another advantage is that since you and your wife had lived in singapore for so long, she cannot file Dowry or Domestic violence cases against you in india. so in all ways your strategy seems perfect and you need to ensure perfect execution of your plan.
Hope this helps