In most cases, immigrating to Canada with minor children poses no great difficulty.
However, when the parents of the child (or children) are no longer together and share custody (or have visitation rights, etc), this can be a serious impediment to immigrating.
For example, if the custodial parent wishes to immigrate to Canada, and the other parent does not want the child or children to immigrate, this situation will be very difficult to overcome.
CIC will want clear permission from the non-custodial parent before issuing any visas. I’ve seen this many times – the non-custodial parent does not have good relations with the custodial parent and decides not to consent to the children immigrating. This places the entire application in jeopardy and can be impossible to overcome.
If you are a custodial parent wishing to immigrate, be sure to discuss this issue with the non-custodial parent well in advance of applying to immigrate. Otherwise, you may go through a lot of time (and money) and be denied if the non-custodial parent does not consent to the children immigrating to Canada.