I agree with armoured that adoption should not be necessary for Canadian immigration purposes. I mentioned adoption because,, in your initial query, you asked about showing your wife as the mother of your son. But I am sure you can come to Canada as a family without any requirement for your wife to adopt your son.
As see it, you should make sure that you have lawful authority to remove your child from India. While canuck78 mentions a bias against fathers, mothers can also get caught. This I know from personal experience. Some time ago, my wife was returning to visit her country wth our kid, who was then about age 3. She had my permission to travel with our child and we had prepared a document evidencing that permission. Unfortunately, the document was sitting on a desk at our home in Vancouver when she was at YVR trying to board a plane. She was not allowed to depart. She and our child had to re-book for 2 days later. We were fortunate that the airline did not make her pay full price for new tickets. We just paid a change fee. But still, a pain.
Nothing canuck78 said in the above passage is wrong, it just might not go far enough. Under Canadian law, sole custody does not endow one with the full bundle of parental rights and responsibilities. That comes with guardianship, a different concept. It was explained by a BC court some time ago, thus:
The importance of guardianship cannot be overstated. It is a broad concept that encompasses the concept of custody and goes further, to include a collection of rights and responsibilities relating to a child, subject to specific statutory limitations. These rights and responsibilities are wide-ranging and relate to all matters that affect the best interests of children. They include, for example, education, religious and health decisions. A guardian has responsibilities not only with respect to the "person" of the child, but also the child's property.
Wong, Re v. S.C., Stromberg-Stein J., Vancouver E002815, E002866, October 20, 2000 , 22pp.
The matter is addressed, in part, in BC's Family Law Act:
Parenting arrangements
40 (1) Only a guardian may have parental responsibilities and parenting time with respect to a child.
Parental responsibilities
41 For the purposes of this Part, parental responsibilities with respect to a child are as follows:
(a)making day-to-day decisions affecting the child and having day-to-day care, control and supervision of the child;
(b)making decisions respecting where the child will reside;
...
(g)applying for a passport, licence, permit, benefit, privilege or other thing for the child;
So, my simple point from the above is that do not place too much reliance in the fact that you have sole custody, unless you also have sole guardianship. Whether the Indian law recognizes the niceties between the two concepts is another issue, as is the matter of whether those you come in contact with at immigration counters, etc. are schooled in family law and international law. But headaches should be avoided if the child's mother is aware of and agrees to travel for the child, and has provided proof of that assent in writing. Probably best in statutory declaration or similar form.
Always a course of prudence. No lies. Not even suppression of the truth.
