I used to be an immigration officer here in Canada, and I saw this from time to time. Our rules sound similar. If a foreigner is coming to Canada to marry a Canadian citizen or permanent resident, they absolutely need signed and notarized permission from the child's second parent to immigrate (and this may be verified with them in-person if there is any doubt). There is no way around it. Predictably, this can lead to extortion tactics - since the divorce was likely nasty, the second parent will let the child leave, but for an exorbitant ransom that takes advantage of the new relationship. It's not fair, but this is why women with children have a much harder time on this site. I, personally, wouldn't get involved with a woman with a child because this can easily lead to devastation.